Daily Papers

Large Language Models (LLMs) have exhibited impressive proficiency in various natural language processing (NLP) tasks, which involve increasingly complex reasoning. Knowledge reasoning, a primary type of reasoning, aims at deriving new knowledge from existing one.While it has been widely studied in the context of knowledge graphs (KGs), knowledge reasoning in LLMs remains underexplored. In this paper, we introduce Chain-of-Knowledge, a comprehensive framework for knowledge reasoning, including methodologies for both dataset construction and model learning. For dataset construction, we create KnowReason via rule mining on KGs. For model learning, we observe rule overfitting induced by naive training. Hence, we enhance CoK with a trial-and-error mechanism that simulates the human process of internal knowledge exploration. We conduct extensive experiments with KnowReason. Our results show the effectiveness of CoK in refining LLMs in not only knowledge reasoning, but also general reasoning benchmarkms.

Intelligence is a crucial trait for species to find solutions within a limited number of trial-and-error attempts. Building on this idea, we introduce Survival Game as a framework to evaluate intelligence based on the number of failed attempts in a trial-and-error process. Fewer failures indicate higher intelligence. When the expectation and variance of failure counts are both finite, it signals the ability to consistently find solutions to new challenges, which we define as the Autonomous Level of intelligence. Using Survival Game, we comprehensively evaluate existing AI systems. Our results show that while AI systems achieve the Autonomous Level in simple tasks, they are still far from it in more complex tasks, such as vision, search, recommendation, and language. While scaling current AI technologies might help, this would come at an astronomical cost. Projections suggest that achieving the Autonomous Level for general tasks would require 10^{26} parameters. To put this into perspective, loading such a massive model requires so many H100 GPUs that their total value is 10^{7} times that of Apple Inc.'s market value. Even with Moore's Law, supporting such a parameter scale would take 70 years. This staggering cost highlights the complexity of human tasks and the inadequacies of current AI technologies. To further investigate this phenomenon, we conduct a theoretical analysis of Survival Game and its experimental results. Our findings suggest that human tasks possess a criticality property. As a result, Autonomous Level requires a deep understanding of the task's underlying mechanisms. Current AI systems, however, do not fully grasp these mechanisms and instead rely on superficial mimicry, making it difficult for them to reach an autonomous level. We believe Survival Game can not only guide the future development of AI but also offer profound insights into human intelligence.

Tools are essential for large language models (LLMs) to acquire up-to-date information and take consequential actions in external environments. Existing work on tool-augmented LLMs primarily focuses on the broad coverage of tools and the flexibility of adding new tools. However, a critical aspect that has surprisingly been understudied is simply how accurately an LLM uses tools for which it has been trained. We find that existing LLMs, including GPT-4 and open-source LLMs specifically fine-tuned for tool use, only reach a correctness rate in the range of 30% to 60%, far from reliable use in practice. We propose a biologically inspired method for tool-augmented LLMs, simulated trial and error (STE), that orchestrates three key mechanisms for successful tool use behaviors in the biological system: trial and error, imagination, and memory. Specifically, STE leverages an LLM's 'imagination' to simulate plausible scenarios for using a tool, after which the LLM interacts with the tool to learn from its execution feedback. Both short-term and long-term memory are employed to improve the depth and breadth of the exploration, respectively. Comprehensive experiments on ToolBench show that STE substantially improves tool learning for LLMs under both in-context learning and fine-tuning settings, bringing a boost of 46.7% to Mistral-Instruct-7B and enabling it to outperform GPT-4. We also show effective continual learning of tools via a simple experience replay strategy.

Current approaches to prosthetic control are limited by their reliance on traditional methods, which lack real-time adaptability and intuitive responsiveness. These limitations are particularly pronounced in assistive technologies designed for individuals with diverse cognitive states and motor intentions. In this paper, we introduce a framework that leverages Reinforcement Learning (RL) with Deep Q-Networks (DQN) for classification tasks. Additionally, we present a preprocessing technique using the Common Spatial Pattern (CSP) for multiclass motor imagery (MI) classification in a One-Versus-The-Rest (OVR) manner. The subsequent 'csp space' transformation retains the temporal dimension of EEG signals, crucial for extracting discriminative features. The integration of DQN with a 1D-CNN-LSTM architecture optimizes the decision-making process in real-time, thereby enhancing the system's adaptability to the user's evolving needs and intentions. We elaborate on the data processing methods for two EEG motor imagery datasets. Our innovative model, RLEEGNet, incorporates a 1D-CNN-LSTM architecture as the Online Q-Network within the DQN, facilitating continuous adaptation and optimization of control strategies through feedback. This mechanism allows the system to learn optimal actions through trial and error, progressively improving its performance. RLEEGNet demonstrates high accuracy in classifying MI-EEG signals, achieving as high as 100% accuracy in MI tasks across both the GigaScience (3-class) and BCI-IV-2a (4-class) datasets. These results highlight the potential of combining DQN with a 1D-CNN-LSTM architecture to significantly enhance the adaptability and responsiveness of BCI systems.

Recent advances in large vision-language models (LVLMs) have shown promise for embodied task planning, yet they struggle with fundamental challenges like dependency constraints and efficiency. Existing approaches either solely optimize action selection or leverage world models during inference, overlooking the benefits of learning to model the world as a way to enhance planning capabilities. We propose Dual Preference Optimization (D^2PO), a new learning framework that jointly optimizes state prediction and action selection through preference learning, enabling LVLMs to understand environment dynamics for better planning. To automatically collect trajectories and stepwise preference data without human annotation, we introduce a tree search mechanism for extensive exploration via trial-and-error. Extensive experiments on VoTa-Bench demonstrate that our D^2PO-based method significantly outperforms existing methods and GPT-4o when applied to Qwen2-VL (7B), LLaVA-1.6 (7B), and LLaMA-3.2 (11B), achieving superior task success rates with more efficient execution paths.

Recent advances in LegalAI have primarily focused on individual case judgment analysis, often overlooking the critical appellate process within the judicial system. Appeals serve as a core mechanism for error correction and ensuring fair trials, making them highly significant both in practice and in research. To address this gap, we present the AppealCase dataset, consisting of 10,000 pairs of real-world, matched first-instance and second-instance documents across 91 categories of civil cases. The dataset also includes detailed annotations along five dimensions central to appellate review: judgment reversals, reversal reasons, cited legal provisions, claim-level decisions, and whether there is new information in the second instance. Based on these annotations, we propose five novel LegalAI tasks and conduct a comprehensive evaluation across 20 mainstream models. Experimental results reveal that all current models achieve less than 50% F1 scores on the judgment reversal prediction task, highlighting the complexity and challenge of the appeal scenario. We hope that the AppealCase dataset will spur further research in LegalAI for appellate case analysis and contribute to improving consistency in judicial decision-making.

We study the problem of designing mechanisms for information acquisition scenarios. This setting models strategic interactions between an uniformed receiver and a set of informed senders. In our model the senders receive information about the underlying state of nature and communicate their observation (either truthfully or not) to the receiver, which, based on this information, selects an action. Our goal is to design mechanisms maximizing the receiver's utility while incentivizing the senders to report truthfully their information. First, we provide an algorithm that efficiently computes an optimal incentive compatible (IC) mechanism. Then, we focus on the online problem in which the receiver sequentially interacts in an unknown game, with the objective of minimizing the cumulative regret w.r.t. the optimal IC mechanism, and the cumulative violation of the incentive compatibility constraints. We investigate two different online scenarios, i.e., the full and bandit feedback settings. For the full feedback problem, we propose an algorithm that guarantees mathcal O(sqrt T) regret and violation, while for the bandit feedback setting we present an algorithm that attains mathcal O(T^{alpha}) regret and mathcal O(T^{1-alpha/2}) violation for any alphain[1/2, 1]. Finally, we complement our results providing a tight lower bound.

Most learning algorithms with formal regret guarantees assume that no mistake is irreparable and essentially rely on trying all possible behaviors. This approach is problematic when some mistakes are catastrophic, i.e., irreparable. We propose an online learning problem where the goal is to minimize the chance of catastrophe. Specifically, we assume that the payoff in each round represents the chance of avoiding catastrophe that round and aim to maximize the product of payoffs (the overall chance of avoiding catastrophe) while allowing a limited number of queries to a mentor. We first show that in general, any algorithm either constantly queries the mentor or is nearly guaranteed to cause catastrophe. However, in settings where the mentor policy class is learnable in the standard online learning model, we provide an algorithm whose regret and rate of querying the mentor both approach 0 as the time horizon grows. Conceptually, if a policy class is learnable in the absence of catastrophic risk, it is learnable in the presence of catastrophic risk if the agent can ask for help.

We study a strategic variant of the multi-armed bandit problem, which we coin the strategic click-bandit. This model is motivated by applications in online recommendation where the choice of recommended items depends on both the click-through rates and the post-click rewards. Like in classical bandits, rewards follow a fixed unknown distribution. However, we assume that the click-rate of each arm is chosen strategically by the arm (e.g., a host on Airbnb) in order to maximize the number of times it gets clicked. The algorithm designer does not know the post-click rewards nor the arms' actions (i.e., strategically chosen click-rates) in advance, and must learn both values over time. To solve this problem, we design an incentive-aware learning algorithm, UCB-S, which achieves two goals simultaneously: (a) incentivizing desirable arm behavior under uncertainty; (b) minimizing regret by learning unknown parameters. We characterize all approximate Nash equilibria among arms under UCB-S and show a mathcal{O} (KT) regret bound uniformly in every equilibrium. We also show that incentive-unaware algorithms generally fail to achieve low regret in the strategic click-bandit. Finally, we support our theoretical results by simulations of strategic arm behavior which confirm the effectiveness and robustness of our proposed incentive design.

Large Language Models (LLMs) are prone to hallucination, especially during multi-hop and reasoning-intensive tasks such as mathematical problem solving. While Outcome Reward Models verify only final answers, Process Reward Models (PRMs) score each intermediate step to steer generation toward coherent solutions. We introduce PathFinder-PRM, a novel hierarchical, error-aware discriminative PRM that first classifies math and consistency errors at each step, then combines these fine-grained signals to estimate step correctness. To train PathFinder-PRM, we construct a 400K-sample dataset by enriching the human-annotated PRM800K corpus and RLHFlow Mistral traces with three-dimensional step-level labels. On PRMBench, PathFinder-PRM achieves a new state-of-the-art PRMScore of 67.7, outperforming the prior best (65.5) while using 3 times less data. When applied to reward guided greedy search, our model yields prm@8 48.3, a +1.5 point gain over the strongest baseline. These results demonstrate that decoupled error detection and reward estimation not only boost fine-grained error detection but also substantially improve end-to-end, reward-guided mathematical reasoning with greater data efficiency.

Implementing a reward function that perfectly captures a complex task in the real world is impractical. As a result, it is often appropriate to think of the reward function as a proxy for the true objective rather than as its definition. We study this phenomenon through the lens of Goodhart's law, which predicts that increasing optimisation of an imperfect proxy beyond some critical point decreases performance on the true objective. First, we propose a way to quantify the magnitude of this effect and show empirically that optimising an imperfect proxy reward often leads to the behaviour predicted by Goodhart's law for a wide range of environments and reward functions. We then provide a geometric explanation for why Goodhart's law occurs in Markov decision processes. We use these theoretical insights to propose an optimal early stopping method that provably avoids the aforementioned pitfall and derive theoretical regret bounds for this method. Moreover, we derive a training method that maximises worst-case reward, for the setting where there is uncertainty about the true reward function. Finally, we evaluate our early stopping method experimentally. Our results support a foundation for a theoretically-principled study of reinforcement learning under reward misspecification.

Large Language Models' (LLM) reasoning can be improved using test-time aggregation strategies, i.e., generating multiple samples and voting among generated samples. While these improve performance, they often reach a saturation point. Refinement offers an alternative by using LLM-generated feedback to improve solution quality. However, refinement introduces 3 key challenges: (1) Excessive refinement: Uniformly refining all instances can over-correct and reduce the overall performance. (2) Inability to localize and address errors: LLMs have a limited ability to self-correct and struggle to identify and correct their own mistakes. (3) Insufficient refinement: Deciding how many iterations of refinement are needed is non-trivial, and stopping too soon could leave errors unaddressed. To tackle these issues, we propose MAgICoRe, which avoids excessive refinement by categorizing problem difficulty as easy or hard, solving easy problems with coarse-grained aggregation and hard ones with fine-grained and iterative multi-agent refinement. To improve error localization, we incorporate external step-wise reward model (RM) scores. Moreover, to ensure effective refinement, we employ a multi-agent loop with three agents: Solver, Reviewer (which generates targeted feedback based on step-wise RM scores), and the Refiner (which incorporates feedback). To ensure sufficient refinement, we re-evaluate updated solutions, iteratively initiating further rounds of refinement. We evaluate MAgICoRe on Llama-3-8B and GPT-3.5 and show its effectiveness across 5 math datasets. Even one iteration of MAgICoRe beats Self-Consistency by 3.4%, Best-of-k by 3.2%, and Self-Refine by 4.0% while using less than half the samples. Unlike iterative refinement with baselines, MAgICoRe continues to improve with more iterations. Finally, our ablations highlight the importance of MAgICoRe's RMs and multi-agent communication.

We investigate the mechanism design problem faced by a principal who hires multiple agents to gather and report costly information. Then, the principal exploits the information to make an informed decision. We model this problem as a game, where the principal announces a mechanism consisting in action recommendations and a payment function, a.k.a. scoring rule. Then, each agent chooses an effort level and receives partial information about an underlying state of nature based on the effort. Finally, the agents report the information (possibly non-truthfully), the principal takes a decision based on this information, and the agents are paid according to the scoring rule. While previous work focuses on single-agent problems, we consider multi-agents settings. This poses the challenge of coordinating the agents' efforts and aggregating correlated information. Indeed, we show that optimal mechanisms must correlate agents' efforts, which introduces externalities among the agents, and hence complex incentive compatibility constraints and equilibrium selection problems. First, we design a polynomial-time algorithm to find an optimal incentive compatible mechanism. Then, we study an online problem, where the principal repeatedly interacts with a group of unknown agents. We design a no-regret algorithm that provides mathcal{O}(T^{2/3}) regret with respect to an optimal mechanism, matching the state-of-the-art bound for single-agent settings.

We study the problem of using low computational cost to automate the choices of learners and hyperparameters for an ad-hoc training dataset and error metric, by conducting trials of different configurations on the given training data. We investigate the joint impact of multiple factors on both trial cost and model error, and propose several design guidelines. Following them, we build a fast and lightweight library FLAML which optimizes for low computational resource in finding accurate models. FLAML integrates several simple but effective search strategies into an adaptive system. It significantly outperforms top-ranked AutoML libraries on a large open source AutoML benchmark under equal, or sometimes orders of magnitude smaller budget constraints.

Past analyses of reinforcement learning from human feedback (RLHF) assume that the human fully observes the environment. What happens when human feedback is based only on partial observations? We formally define two failure cases: deception and overjustification. Modeling the human as Boltzmann-rational w.r.t. a belief over trajectories, we prove conditions under which RLHF is guaranteed to result in policies that deceptively inflate their performance, overjustify their behavior to make an impression, or both. To help address these issues, we mathematically characterize how partial observability of the environment translates into (lack of) ambiguity in the learned return function. In some cases, accounting for partial observability makes it theoretically possible to recover the return function and thus the optimal policy, while in other cases, there is irreducible ambiguity. We caution against blindly applying RLHF in partially observable settings and propose research directions to help tackle these challenges.

Large language models (LLMs) have demonstrated strong reasoning abilities in mathematical tasks, often enhanced through reinforcement learning (RL). However, RL-trained models frequently produce unnecessarily long reasoning traces -- even for simple queries -- leading to increased inference costs and latency. While recent approaches attempt to control verbosity by adding length penalties to the reward function, these methods rely on fixed penalty terms that are hard to tune and cannot adapt as the model's reasoning capability evolves, limiting their effectiveness. In this work, we propose an adaptive reward-shaping method that enables LLMs to "think fast and right" -- producing concise outputs without sacrificing correctness. Our method dynamically adjusts the reward trade-off between accuracy and response length based on model performance: when accuracy is high, the length penalty increases to encourage faster length reduction; when accuracy drops, the penalty is relaxed to preserve correctness. This adaptive reward accelerates early-stage length reduction while avoiding over-compression in later stages. Experiments across multiple datasets show that our approach consistently and dramatically reduces reasoning length while largely maintaining accuracy, offering a new direction for cost-efficient adaptive reasoning in large-scale language models.

Reward models are key in reinforcement learning from human feedback (RLHF) systems, aligning the model behavior with human preferences. Particularly in the math domain, there have been plenty of studies using reward models to align policies for improving reasoning capabilities. Recently, as the importance of reward models has been emphasized, RewardBench is proposed to understand their behavior. However, we figure out that the math subset of RewardBench has different representations between chosen and rejected completions, and relies on a single comparison, which may lead to unreliable results as it only see an isolated case. Therefore, it fails to accurately present the robustness of reward models, leading to a misunderstanding of its performance and potentially resulting in reward hacking. In this work, we introduce a new design for reliable evaluation of reward models, and to validate this, we construct RewardMATH, a benchmark that effectively represents the robustness of reward models in mathematical reasoning tasks. We demonstrate that the scores on RewardMATH strongly correlate with the results of optimized policy and effectively estimate reward overoptimization, whereas the existing benchmark shows almost no correlation. The results underscore the potential of our design to enhance the reliability of evaluation, and represent the robustness of reward model. We make our code and data publicly available.

This paper presents a case study of coding tasks by the latest reasoning models of OpenAI, i.e. o1-preview and o1-mini, in comparison with other frontier models. The o1 models deliver SOTA results for WebApp1K, a single-task benchmark. To this end, we introduce WebApp1K-Duo, a harder benchmark doubling number of tasks and test cases. The new benchmark causes the o1 model performances to decline significantly, falling behind Claude 3.5. Moreover, they consistently fail when confronted with atypical yet correct test cases, a trap non-reasoning models occasionally avoid. We hypothesize that the performance variability is due to instruction comprehension. Specifically, the reasoning mechanism boosts performance when all expectations are captured, meanwhile exacerbates errors when key expectations are missed, potentially impacted by input lengths. As such, we argue that the coding success of reasoning models hinges on the top-notch base model and SFT to ensure meticulous adherence to instructions.

Machine learning models always make a prediction, even when it is likely to be inaccurate. This behavior should be avoided in many decision support applications, where mistakes can have severe consequences. Albeit already studied in 1970, machine learning with rejection recently gained interest. This machine learning subfield enables machine learning models to abstain from making a prediction when likely to make a mistake. This survey aims to provide an overview on machine learning with rejection. We introduce the conditions leading to two types of rejection, ambiguity and novelty rejection, which we carefully formalize. Moreover, we review and categorize strategies to evaluate a model's predictive and rejective quality. Additionally, we define the existing architectures for models with rejection and describe the standard techniques for learning such models. Finally, we provide examples of relevant application domains and show how machine learning with rejection relates to other machine learning research areas.

Machine learning models are routinely used to support decisions that affect individuals -- be it to screen a patient for a serious illness or to gauge their response to treatment. In these tasks, we are limited to learning models from datasets with noisy labels. In this paper, we study the instance-level impact of learning under label noise. We introduce a notion of regret for this regime, which measures the number of unforeseen mistakes due to noisy labels. We show that standard approaches to learning under label noise can return models that perform well at a population-level while subjecting individuals to a lottery of mistakes. We present a versatile approach to estimate the likelihood of mistakes at the individual-level from a noisy dataset by training models over plausible realizations of datasets without label noise. This is supported by a comprehensive empirical study of label noise in clinical prediction tasks. Our results reveal how failure to anticipate mistakes can compromise model reliability and adoption -- we demonstrate how we can address these challenges by anticipating and avoiding regretful decisions.

Error Feedback (EF) is a highly popular and immensely effective mechanism for fixing convergence issues which arise in distributed training methods (such as distributed GD or SGD) when these are enhanced with greedy communication compression techniques such as TopK. While EF was proposed almost a decade ago (Seide et al., 2014), and despite concentrated effort by the community to advance the theoretical understanding of this mechanism, there is still a lot to explore. In this work we study a modern form of error feedback called EF21 (Richtarik et al., 2021) which offers the currently best-known theoretical guarantees, under the weakest assumptions, and also works well in practice. In particular, while the theoretical communication complexity of EF21 depends on the quadratic mean of certain smoothness parameters, we improve this dependence to their arithmetic mean, which is always smaller, and can be substantially smaller, especially in heterogeneous data regimes. We take the reader on a journey of our discovery process. Starting with the idea of applying EF21 to an equivalent reformulation of the underlying problem which (unfortunately) requires (often impractical) machine cloning, we continue to the discovery of a new weighted version of EF21 which can (fortunately) be executed without any cloning, and finally circle back to an improved analysis of the original EF21 method. While this development applies to the simplest form of EF21, our approach naturally extends to more elaborate variants involving stochastic gradients and partial participation. Further, our technique improves the best-known theory of EF21 in the rare features regime (Richtarik et al., 2023). Finally, we validate our theoretical findings with suitable experiments.

Although large language models (LLMs) have become transformative, they still make mistakes and can explore unproductive reasoning paths. Self-correction is an important capability for a trustworthy LLM, particularly an autoregressive LLM. While LLMs can identify error in user input, they exhibit a systematic 'Self-Correction Blind Spot' - failing to correct identical error in their own outputs. To systematically study this phenomenon, we introduce Self-Correction Bench, a systematic framework to measure this phenomenon through controlled error injection at three complexity levels. Testing 14 models, we find an average 64.5% blind spot rate. We find multiple evidences that this limitation relates to training data composition: human training demonstrations predominantly show error-free responses rather than error-correction sequences, unlike RL-trained models that learn error correction through outcome feedback. Remarkably, simply appending "Wait" reduces blind spots by 89.3%, suggesting that the capability exists but requires activation. Our work highlights a critical limitation in current LLMs and offers potential avenues for improving their reliability and trustworthiness.

Process-level Reward Models (PRMs) are crucial for complex reasoning and decision-making tasks, where each intermediate step plays an important role in the reasoning process. Since language models are prone to various types of errors during the reasoning process, PRMs are required to possess nuanced capabilities for detecting various implicit error types in real-world scenarios. However, current benchmarks primarily focus on step correctness, failing to evaluate PRMs' performance systematically. To address this gap, we introduce PRMBench, a process-level benchmark specifically designed to assess the fine-grained error detection capabilities of PRMs. PRMBench comprises 6,216 carefully designed problems and 83,456 step-level labels, evaluating models across multiple dimensions, including simplicity, soundness, and sensitivity. In our experiments on 15 models, spanning both open-source PRMs and closed-source large language models prompted as critic models, we uncover significant weaknesses in current PRMs. These findings underscore the challenges inherent in process-level evaluation and highlight key directions for future research. We hope PRMBench can be a robust bench for advancing research on PRM evaluation and development.

Recent advancements in reinforcement learning (RL) for large language models (LLMs), exemplified by DeepSeek R1, have shown that even a simple question-answering task can substantially improve an LLM's reasoning capabilities. In this work, we extend this approach by modifying the task into a multi-attempt setting. Instead of generating a single response per question, the model is given multiple attempts, with feedback provided after incorrect responses. The multi-attempt task encourages the model to refine its previous attempts and improve search efficiency. Experimental results show that even a small LLM trained on a multi-attempt task achieves significantly higher accuracy when evaluated with more attempts, improving from 45.6% with 1 attempt to 52.5% with 2 attempts on the math benchmark. In contrast, the same LLM trained on a standard single-turn task exhibits only a marginal improvement, increasing from 42.3% to 43.2% when given more attempts during evaluation. The results indicate that, compared to the standard single-turn task, an LLM trained on a multi-attempt task achieves slightly better performance on math benchmarks while also learning to refine its responses more effectively based on user feedback. Full code is available at https://github.com/DualityRL/multi-attempt

The success of Reinforcement Learning from Human Feedback (RLHF) critically depends on the quality of the reward model. While this quality is primarily evaluated through accuracy, it remains unclear whether accuracy fully captures what makes a reward model an effective teacher. We address this question from an optimization perspective. First, we prove that regardless of how accurate a reward model is, if it induces low reward variance, then the RLHF objective suffers from a flat landscape. Consequently, even a perfectly accurate reward model can lead to extremely slow optimization, underperforming less accurate models that induce higher reward variance. We additionally show that a reward model that works well for one language model can induce low reward variance, and thus a flat objective landscape, for another. These results establish a fundamental limitation of evaluating reward models solely based on accuracy or independently of the language model they guide. Experiments using models of up to 8B parameters corroborate our theory, demonstrating the interplay between reward variance, accuracy, and reward maximization rate. Overall, our findings highlight that beyond accuracy, a reward model needs to induce sufficient variance for efficient optimization.

Large language models (LLMs) have demonstrated remarkable reasoning capability in solving mathematical problems. However, existing approaches primarily focus on improving the quality of correct training data, e.g., distilling high-quality correct solutions from advanced models, neglecting the value contained in error data, potentially hindering the model's reflective ability. Though some studies attempt to leverage error data, they often involve complex mechanisms, such as Monte Carlo Tree Search (MCTS) to explore error nodes. In this work, we propose to enhance LLMs' reasoning ability by Learning from Errors for Mathematical Advancement (LEMMA). LEMMA constructs data consisting of an incorrect solution with an erroneous step and a reflection connection to a correct solution for fine-tuning. Specifically, we systematically analyze the model-generated error types and introduce an error-type grounded mistake augmentation method to collect diverse and representative errors. Correct solutions are either from fixing the errors or generating a fresh start. Through a model-aware smooth reflection connection, the erroneous solution is transferred to the correct one. By fine-tuning on the constructed dataset, the model is able to self-correct errors autonomously within the generation process without relying on external critique models. Experimental results demonstrate that LEMMA achieves significant performance improvements over other strong baselines.

Large reasoning models (LRMs) achieve remarkable performance via long reasoning chains, but often incur excessive computational overhead due to redundant reasoning, especially on simple tasks. In this work, we systematically quantify the upper bounds of LRMs under both Long-Thinking and No-Thinking modes, and uncover the phenomenon of "Internal Self-Recovery Mechanism" where models implicitly supplement reasoning during answer generation. Building on this insight, we propose Adaptive Self-Recovery Reasoning (ASRR), a framework that suppresses unnecessary reasoning and enables implicit recovery. By introducing accuracy-aware length reward regulation, ASRR adaptively allocates reasoning effort according to problem difficulty, achieving high efficiency with negligible performance sacrifice. Experiments across multiple benchmarks and models show that, compared with GRPO, ASRR reduces reasoning budget by up to 32.5% (1.5B) and 25.7% (7B) with minimal accuracy loss (1.2% and 0.6% pass@1), and significantly boosts harmless rates on safety benchmarks (up to +21.7%). Our results highlight the potential of ASRR for enabling efficient, adaptive, and safer reasoning in LRMs.

Reinforcement learning from human feedback (RLHF) has emerged as a powerful technique to make large language models (LLMs) more capable in complex settings. RLHF proceeds as collecting human preference data, training a reward model on said data, and optimizing a base ML model with respect to said reward for extrinsic evaluation metrics (e.g. MMLU, GSM8k). RLHF relies on many assumptions about how the various pieces fit together, such as a reward model capturing human preferences and an RL optimizer extracting the right signal from a reward model. As the RLHF process involves many distinct design decisions, it is easy to assume that multiple processes are correlated and therefore numerically linked. This apparent correlation is often not true, where reward models are easily overoptimized or RL optimizers can reduce performance on tasks not modeled in the data. Notable manifestations of models trained with imperfect RLHF systems are those that are prone to refusing basic requests for safety reasons or appearing lazy in generations. As chat model evaluation becomes increasingly nuanced, the reliance on a perceived link between reward model training, RL scores, and downstream performance drives these issues, which we describe as an objective mismatch. In this paper, we illustrate the causes of this issue, reviewing relevant literature from model-based reinforcement learning, and argue for solutions. By solving objective mismatch in RLHF, the ML models of the future will be more precisely aligned to user instructions for both safety and helpfulness.

Reward models have been increasingly critical for improving the reasoning capability of LLMs. Existing research has shown that a well-trained reward model can substantially improve model performances at inference time via search. However, the potential of reward models during RL training time still remains largely under-explored. It is currently unclear whether these reward models can provide additional training signals to enhance the reasoning capabilities of LLMs in RL training that uses sparse success rewards, which verify the correctness of solutions. In this work, we evaluate popular reward models for RL training, including the Outcome-supervised Reward Model (ORM) and the Process-supervised Reward Model (PRM), and train a collection of LLMs for math problems using RL by combining these learned rewards with success rewards. Surprisingly, even though these learned reward models have strong inference-time performances, they may NOT help or even hurt RL training, producing worse performances than LLMs trained with the success reward only. Our analysis reveals that an LLM can receive high rewards from some of these reward models by repeating correct but unnecessary reasoning steps, leading to a severe reward hacking issue. Therefore, we introduce two novel reward refinement techniques, including Clipping and Delta. The key idea is to ensure the accumulative reward of any reasoning trajectory is upper-bounded to keep a learned reward model effective without being exploited. We evaluate our techniques with multiple reward models over a set of 1.5B and 7B LLMs on MATH and GSM8K benchmarks and demonstrate that with a carefully designed reward function, RL training without any additional supervised tuning can improve all the evaluated LLMs, including the state-of-the-art 7B LLM Qwen2.5-Math-7B-Instruct on MATH and GSM8K benchmarks.

Large Language Models (LLMs) agents are increasingly pivotal for addressing complex tasks in interactive environments. Existing work mainly focuses on enhancing performance through behavior cloning from stronger experts, yet such approaches often falter in real-world applications, mainly due to the inability to recover from errors. However, step-level critique data is difficult and expensive to collect. Automating and dynamically constructing self-critique datasets is thus crucial to empowering models with intelligent agent capabilities. In this work, we propose an iterative self-training framework, Agent-R, that enables language Agent to Reflect on the fly. Unlike traditional methods that reward or penalize actions based on correctness, Agent-R leverages MCTS to construct training data that recover correct trajectories from erroneous ones. A key challenge of agent reflection lies in the necessity for timely revision rather than waiting until the end of a rollout. To address this, we introduce a model-guided critique construction mechanism: the actor model identifies the first error step (within its current capability) in a failed trajectory. Starting from it, we splice it with the adjacent correct path, which shares the same parent node in the tree. This strategy enables the model to learn reflection based on its current policy, therefore yielding better learning efficiency. To further explore the scalability of this self-improvement paradigm, we investigate iterative refinement of both error correction capabilities and dataset construction. Our findings demonstrate that Agent-R continuously improves the model's ability to recover from errors and enables timely error correction. Experiments on three interactive environments show that Agent-R effectively equips agents to correct erroneous actions while avoiding loops, achieving superior performance compared to baseline methods (+5.59%).

To enhance the efficiency and practicality of federated bandit learning, recent advances have introduced incentives to motivate communication among clients, where a client participates only when the incentive offered by the server outweighs its participation cost. However, existing incentive mechanisms naively assume the clients are truthful: they all report their true cost and thus the higher cost one participating client claims, the more the server has to pay. Therefore, such mechanisms are vulnerable to strategic clients aiming to optimize their own utility by misreporting. To address this issue, we propose an incentive compatible (i.e., truthful) communication protocol, named Truth-FedBan, where the incentive for each participant is independent of its self-reported cost, and reporting the true cost is the only way to achieve the best utility. More importantly, Truth-FedBan still guarantees the sub-linear regret and communication cost without any overheads. In other words, the core conceptual contribution of this paper is, for the first time, demonstrating the possibility of simultaneously achieving incentive compatibility and nearly optimal regret in federated bandit learning. Extensive numerical studies further validate the effectiveness of our proposed solution.

Large language models have shown promise in clinical decision making, but current approaches struggle to localize and correct errors at specific steps of the reasoning process. This limitation is critical in medicine, where identifying and addressing reasoning errors is essential for accurate diagnosis and effective patient care. We introduce Med-PRM, a process reward modeling framework that leverages retrieval-augmented generation to verify each reasoning step against established medical knowledge bases. By verifying intermediate reasoning steps with evidence retrieved from clinical guidelines and literature, our model can precisely assess the reasoning quality in a fine-grained manner. Evaluations on five medical QA benchmarks and two open-ended diagnostic tasks demonstrate that Med-PRM achieves state-of-the-art performance, with improving the performance of base models by up to 13.50% using Med-PRM. Moreover, we demonstrate the generality of Med-PRM by integrating it in a plug-and-play fashion with strong policy models such as Meerkat, achieving over 80\% accuracy on MedQA for the first time using small-scale models of 8 billion parameters. Our code and data are available at: https://med-prm.github.io/

As language models regularly make mistakes when solving math problems, automated identification of errors in the reasoning process becomes increasingly significant for their scalable oversight. In this paper, we introduce ProcessBench for measuring the ability to identify erroneous steps in mathematical reasoning. It consists of 3,400 test cases, primarily focused on competition- and Olympiad-level math problems. Each test case contains a step-by-step solution with error location annotated by human experts. Models are required to identify the earliest step that contains an error, or conclude that all steps are correct. We conduct extensive evaluation on ProcessBench, involving two types of models: process reward models (PRMs) and critic models, where for the latter we prompt general language models to critique each solution step by step. We draw two main observations: (1) Existing PRMs typically fail to generalize to more challenging math problems beyond GSM8K and MATH. They underperform both critic models (i.e., prompted general language models) and our own trained PRM that is straightforwardly fine-tuned on the PRM800K dataset. (2) The best open-source model, QwQ-32B-Preview, has demonstrated the critique capability competitive with the proprietary model GPT-4o, despite that it still lags behind the reasoning-specialized o1-mini. We hope ProcessBench can foster future research in reasoning process assessment, paving the way toward scalable oversight of language models.

While self-correction has shown promise in improving LLM outputs in terms of style and quality (e.g. Chen et al., 2023; Madaan et al., 2023), recent attempts to self-correct logical or reasoning errors often cause correct answers to become incorrect, resulting in worse performances overall (Huang et al., 2023). In this paper, we break down the self-correction process into two core components: mistake finding and output correction. For mistake finding, we release BIG-Bench Mistake, a dataset of logical mistakes in Chain-of-Thought reasoning traces. We provide benchmark numbers for several state-of-the-art LLMs, and demonstrate that LLMs generally struggle with finding logical mistakes. For output correction, we propose a backtracking method which provides large improvements when given information on mistake location. We construe backtracking as a lightweight alternative to reinforcement learning methods, and show that it remains effective with a reward model at 60-70% accuracy.

Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving. Nevertheless, their full potential, particularly concerning the mitigation of hallucinations and refinement through prover error messages, remains an area that has yet to be thoroughly investigated. To enhance the effectiveness of LLMs in the field, we introduce the Lyra, a new framework that employs two distinct correction mechanisms: Tool Correction (TC) and Conjecture Correction (CC). To implement Tool Correction in the post-processing of formal proofs, we leverage prior knowledge to utilize predefined prover tools (e.g., Sledgehammer) for guiding the replacement of incorrect tools. Tool Correction significantly contributes to mitigating hallucinations, thereby improving the overall accuracy of the proof. In addition, we introduce Conjecture Correction, an error feedback mechanism designed to interact with prover to refine formal proof conjectures with prover error messages. Compared to the previous refinement framework, the proposed Conjecture Correction refines generation with instruction but does not collect paired (generation, error & refinement) prompts. Our method has achieved state-of-the-art (SOTA) performance on both miniF2F validation (48.0% -> 55.3%) and test (45.5% -> 51.2%). We also present 3 IMO problems solved by Lyra. We believe Tool Correction (post-process for hallucination mitigation) and Conjecture Correction (subgoal adjustment from interaction with environment) could provide a promising avenue for future research in this field.

In this work, we study the issue of reward hacking on the response length, a challenge emerging in Reinforcement Learning from Human Feedback (RLHF) on LLMs. A well-formatted, verbose but less helpful response from the LLMs can often deceive LLMs or even human evaluators to achieve high scores. The same issue also holds for some reward models in RL. To address the challenges in both training and evaluation, we establish a more reliable evaluation protocol for comparing different training configurations, which inspects the trade-off between LLM evaluation score and response length obtained by varying training hyperparameters. Based on this evaluation, we conduct large-scale studies, where the results shed insights into the efficacy of hyperparameters and tricks used in RL on mitigating length bias. We further propose to improve the reward model by jointly training two linear heads on shared feature representations to predict the rewards, one trained to correlate with length, and the other trained to decorrelate with length and therefore focus more on the actual content. We then discard the length head in RL to prevent reward hacking on length. Experiments demonstrate that our approach almost eliminates the reward correlation with length, and improves the obtained policy by a significant margin.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

State-of-the-art language models can exhibit impressive reasoning refinement capabilities on math, science or coding tasks. However, recent work demonstrates that even the best models struggle to identify when and where to refine without access to external feedback. Outcome-based Reward Models (ORMs), trained to predict correctness of the final answer indicating when to refine, offer one convenient solution for deciding when to refine. Process Based Reward Models (PRMs), trained to predict correctness of intermediate steps, can then be used to indicate where to refine. But they are expensive to train, requiring extensive human annotations. In this paper, we propose Stepwise ORMs (SORMs) which are trained, only on synthetic data, to approximate the expected future reward of the optimal policy or V^{star}. More specifically, SORMs are trained to predict the correctness of the final answer when sampling the current policy many times (rather than only once as in the case of ORMs). Our experiments show that SORMs can more accurately detect incorrect reasoning steps compared to ORMs, thus improving downstream accuracy when doing refinements. We then train global refinement models, which take only the question and a draft solution as input and predict a corrected solution, and local refinement models which also take as input a critique indicating the location of the first reasoning error. We generate training data for both models synthetically by reusing data used to train the SORM. We find combining global and local refinements, using the ORM as a reranker, significantly outperforms either one individually, as well as a best of three sample baseline. With this strategy we can improve the accuracy of a LLaMA-2 13B model (already fine-tuned with RL) on GSM8K from 53\% to 65\% when greedily sampled.

The rapid emergence of diverse large language models (LLMs) has spurred the development of LLM routers that assign user queries to the most suitable model. However, existing LLM routers typically perform a single-round, one-to-one mapping (i.e., assigning each query to a single model in isolation), which limits their capability to tackle complex tasks that demand the complementary strengths of multiple LLMs. In this paper, we present Router-R1, a reinforcement learning (RL)-based framework that formulates multi-LLM routing and aggregation as a sequential decision process. Router-R1 instantiates the router itself as a capable LLM, leveraging its reasoning ability to interleave "think" actions (internal deliberation) with "route" actions (dynamic model invocation), and integrates each response into its evolving context. To guide learning, we employ a lightweight rule-based reward comprising format rewards, final outcome rewards, and a novel cost reward for performance and cost trade-off optimization, opening a pathway toward optimizing performance-cost tradeoffs via RL. Router-R1 also conditions only on simple model descriptors such as pricing, latency, and example performance, enabling strong generalization to unseen model selection. Experiments on seven general and multi-hop QA benchmarks show that Router-R1 outperforms over several strong baselines, achieving superior performance while maintaining robust generalization and cost management.Code is available at https://github.com/ulab-uiuc/Router-R1.

Reinforcement learning (RL) agents improve through trial-and-error, but when reward is sparse and the agent cannot discover successful action sequences, learning stagnates. This has been a notable problem in training deep RL agents to perform web-based tasks, such as booking flights or replying to emails, where a single mistake can ruin the entire sequence of actions. A common remedy is to "warm-start" the agent by pre-training it to mimic expert demonstrations, but this is prone to overfitting. Instead, we propose to constrain exploration using demonstrations. From each demonstration, we induce high-level "workflows" which constrain the allowable actions at each time step to be similar to those in the demonstration (e.g., "Step 1: click on a textbox; Step 2: enter some text"). Our exploration policy then learns to identify successful workflows and samples actions that satisfy these workflows. Workflows prune out bad exploration directions and accelerate the agent's ability to discover rewards. We use our approach to train a novel neural policy designed to handle the semi-structured nature of websites, and evaluate on a suite of web tasks, including the recent World of Bits benchmark. We achieve new state-of-the-art results, and show that workflow-guided exploration improves sample efficiency over behavioral cloning by more than 100x.

In real world software development, improper or missing exception handling can severely impact the robustness and reliability of code. Exception handling mechanisms require developers to detect, capture, and manage exceptions according to high standards, but many developers struggle with these tasks, leading to fragile code. This problem is particularly evident in open-source projects and impacts the overall quality of the software ecosystem. To address this challenge, we explore the use of large language models (LLMs) to improve exception handling in code. Through extensive analysis, we identify three key issues: Insensitive Detection of Fragile Code, Inaccurate Capture of Exception Block, and Distorted Handling Solution. These problems are widespread across real world repositories, suggesting that robust exception handling practices are often overlooked or mishandled. In response, we propose Seeker, a multi-agent framework inspired by expert developer strategies for exception handling. Seeker uses agents: Scanner, Detector, Predator, Ranker, and Handler to assist LLMs in detecting, capturing, and resolving exceptions more effectively. Our work is the first systematic study on leveraging LLMs to enhance exception handling practices in real development scenarios, providing valuable insights for future improvements in code reliability.

In real world software development, improper or missing exception handling can severely impact the robustness and reliability of code. Exception handling mechanisms require developers to detect, capture, and manage exceptions according to high standards, but many developers struggle with these tasks, leading to fragile code. This problem is particularly evident in open source projects and impacts the overall quality of the software ecosystem. To address this challenge, we explore the use of large language models (LLMs) to improve exception handling in code. Through extensive analysis, we identify three key issues: Insensitive Detection of Fragile Code, Inaccurate Capture of Exception Types, and Distorted Handling Solutions. These problems are widespread across real world repositories, suggesting that robust exception handling practices are often overlooked or mishandled. In response, we propose Seeker, a multi agent framework inspired by expert developer strategies for exception handling. Seeker uses agents: Scanner, Detector, Predator, Ranker, and Handler to assist LLMs in detecting, capturing, and resolving exceptions more effectively. Our work is the first systematic study on leveraging LLMs to enhance exception handling practices, providing valuable insights for future improvements in code reliability.

The reasoning capabilities of large language models (LLMs) have been a longstanding focus of research. Recent works have further enhanced these capabilities using reinforcement learning (RL), with many new methods claiming significant improvements with minimal or no external supervision. Surprisingly, some studies even suggest that random or incorrect reward signals can enhance reasoning performance. However, these breakthroughs are mostly reported on the Qwen2.5 model family and evaluated on well-known benchmarks such as MATH-500, AMC, and AIME, while failing to achieve similar gains on other models like Llama, which warrants further investigation. Our analysis shows that although Qwen2.5 achieves strong mathematical reasoning performance, its pretraining on large-scale web corpora makes it vulnerable to data contamination in popular benchmarks. As a result, results derived from these benchmarks may be unreliable. To address this, we introduce a generator that produces fully synthetic arithmetic problems of arbitrary length and difficulty, yielding a clean dataset we call RandomCalculation. Using these leakage-free datasets, we show that only accurate reward signals consistently improve performance, while noisy or incorrect signals do not. We advocate for evaluating RL methods on uncontaminated benchmarks and across diverse model families to ensure trustworthy conclusions.

Recent studies have shown LLMs possess some ability to improve their responses when given external feedback. However, it remains unclear how effectively and thoroughly these models can incorporate extrinsic feedback. In an ideal scenario, if LLMs receive near-perfect and complete feedback, we would expect them to fully integrate the feedback and change their incorrect answers to correct ones. In this paper, we systematically investigate LLMs' ability to incorporate feedback by designing a controlled experimental environment. For each problem, a solver model attempts a solution, then a feedback generator with access to near-complete ground-truth answers produces targeted feedback, after which the solver tries again. We evaluate this pipeline across a diverse range of tasks, including math reasoning, knowledge reasoning, scientific reasoning, and general multi-domain evaluations with state-of-the-art language models including Claude 3.7 (with and without extended thinking). Surprisingly, even under these near-ideal conditions, solver models consistently show resistance to feedback, a limitation that we term FEEDBACK FRICTION. To mitigate this limitation, we experiment with sampling-based strategies like progressive temperature increases and explicit rejection of previously attempted incorrect answers, which yield improvements but still fail to help models achieve target performance. We also perform a rigorous exploration of potential causes of FEEDBACK FRICTION, ruling out factors such as model overconfidence and data familiarity. We hope that highlighting this issue in LLMs and ruling out several apparent causes will help future research in self-improvement.

Reasoning large language models (LLMs) excel in complex tasks, which has drawn significant attention to reinforcement learning (RL) for LLMs. However, existing approaches allocate an equal number of rollouts to all questions during the RL process, which is inefficient. This inefficiency stems from the fact that training on simple questions yields limited gains, whereas more rollouts are needed for challenging questions to sample correct answers. Furthermore, while RL improves response precision, it limits the model's exploration ability, potentially resulting in a performance cap below that of the base model prior to RL. To address these issues, we propose a mechanism for dynamically allocating rollout budgets based on the difficulty of the problems, enabling more efficient RL training. Additionally, we introduce an adaptive dynamic temperature adjustment strategy to maintain the entropy at a stable level, thereby encouraging sufficient exploration. This enables LLMs to improve response precision while preserving their exploratory ability to uncover potential correct pathways. The code and data is available on: https://github.com/LiaoMengqi/E3-RL4LLMs

Standard practice within Reinforcement Learning from Human Feedback (RLHF) involves optimizing against a Reward Model (RM), which itself is trained to reflect human preferences for desirable generations. A notable subject that is understudied is the (in-)consistency of RMs -- whether they can recognize the semantic changes to different prompts and appropriately adapt their reward assignments -- and their impact on the downstream RLHF model. In this paper, we visit a series of research questions relevant to RM inconsistency: (1) How can we measure the consistency of reward models? (2) How consistent are the existing RMs and how can we improve them? (3) In what ways does reward inconsistency influence the chatbots resulting from the RLHF model training? We propose Contrast Instructions -- a benchmarking strategy for the consistency of RM. Each example in Contrast Instructions features a pair of lexically similar instructions with different ground truth responses. A consistent RM is expected to rank the corresponding instruction and response higher than other combinations. We observe that current RMs trained with the standard ranking objective fail miserably on Contrast Instructions compared to average humans. To show that RM consistency can be improved efficiently without using extra training budget, we propose two techniques ConvexDA and RewardFusion, which enhance reward consistency through extrapolation during the RM training and inference stage, respectively. We show that RLHF models trained with a more consistent RM yield more useful responses, suggesting that reward inconsistency exhibits a trickle-down effect on the downstream RLHF process.

Reinforcement Learning (RL) with unit test feedback has enhanced large language models (LLMs) code generation, but relies on sparse rewards provided only after complete code evaluation, limiting learning efficiency and incremental improvements. When generated code fails all unit tests, no learning signal is received, hindering progress on complex tasks. To address this, we propose a Process Reward Model (PRM) that delivers dense, line-level feedback on code correctness during generation, mimicking human code refinement and providing immediate guidance. We explore various strategies for training PRMs and integrating them into the RL framework, finding that using PRMs both as dense rewards and for value function initialization significantly boosts performance. Our approach increases our in-house LLM's pass rate from 28.2% to 29.8% on LiveCodeBench and from 31.8% to 35.8% on our internal benchmark. Our experimental results highlight the effectiveness of PRMs in enhancing RL-driven code generation, especially for long-horizon scenarios.

Reinforcement learning from human feedback (RLHF) is one of the key techniques that helps large language models (LLMs) to follow instructions and provide helpful and harmless responses. While direct policy optimization methods exist, state-of-the-art LLMs adopt RL-based methods (usually PPO) in RLHF to train the policy to generate good responses guided by a reward model learned from preference data. The main challenge of these methods is the inaccuracy of the intermediate reward model, especially in code generation tasks that require long and complex reasoning to score a response. We find that the reliability of the reward model varies across responses assigned with different rewards. This motivates us to filter the samples whose rewards may be unreliable to improve signal-to-noise ratio during policy learning, resulting in Policy Filtration for Proximal Policy Optimization (PF-PPO). To choose a proper policy filtration strategy for a given reward model, the coefficient of determination (R^2) between rewards and actual scores on filtered samples serves as a good metrics and helps us find several promising strategies. We provide extensive experiments to validate the effectiveness of PF-PPO in code generation tasks, and find that some variants of PF-PPO are highly effective and achieve new state-of-the-art performance across 7-billion-parameter models on HumanEval, MBPP, and a new and more challenging LeetCode Contest benchmark.

Real-world reinforcement learning (RL) is often severely limited since typical RL algorithms heavily rely on the reset mechanism to sample proper initial states. In practice, the reset mechanism is expensive to implement due to the need for human intervention or heavily engineered environments. To make learning more practical, we propose a generic no-regret reduction to systematically design reset-free RL algorithms. Our reduction turns reset-free RL into a two-player game. We show that achieving sublinear regret in this two-player game would imply learning a policy that has both sublinear performance regret and sublinear total number of resets in the original RL problem. This means that the agent eventually learns to perform optimally and avoid resets. By this reduction, we design an instantiation for linear Markov decision processes, which is the first provably correct reset-free RL algorithm to our knowledge.

Reward models (RMs) are at the crux of successful RLHF to align pretrained models to human preferences, yet there has been relatively little study that focuses on evaluation of those reward models. Evaluating reward models presents an opportunity to understand the opaque technologies used for alignment of language models and which values are embedded in them. To date, very few descriptors of capabilities, training methods, or open-source reward models exist. In this paper, we present RewardBench, a benchmark dataset and code-base for evaluation, to enhance scientific understanding of reward models. The RewardBench dataset is a collection of prompt-win-lose trios spanning chat, reasoning, and safety, to benchmark how reward models perform on challenging, structured and out-of-distribution queries. We created specific comparison datasets for RMs that have subtle, but verifiable reasons (e.g. bugs, incorrect facts) why one answer should be preferred to another. On the RewardBench leaderboard, we evaluate reward models trained with a variety of methods, such as the direct MLE training of classifiers and the implicit reward modeling of Direct Preference Optimization (DPO), and on a spectrum of datasets. We present many findings on propensity for refusals, reasoning limitations, and instruction following shortcomings of various reward models towards a better understanding of the RLHF process.

We show that reinforcement learning with verifiable rewards (RLVR) can elicit strong mathematical reasoning in certain models even with spurious rewards that have little, no, or even negative correlation with the correct answer. For example, RLVR improves MATH-500 performance for Qwen2.5-Math-7B in absolute points by 21.4% (random reward), 13.8% (format reward), 24.1% (incorrect label), 26.0% (1-shot RL), and 27.1% (majority voting) -- nearly matching the 29.1% gained with ground truth rewards. However, the spurious rewards that work for Qwen often fail to yield gains with other model families like Llama3 or OLMo2. In particular, we find code reasoning -- thinking in code without actual code execution -- to be a distinctive Qwen2.5-Math behavior that becomes significantly more frequent after RLVR, from 65% to over 90%, even with spurious rewards. Overall, we hypothesize that, given the lack of useful reward signal, RLVR must somehow be surfacing useful reasoning representations learned during pretraining, although the exact mechanism remains a topic for future work. We suggest that future RLVR research should possibly be validated on diverse models rather than a single de facto choice, as we show that it is easy to get significant performance gains on Qwen models even with completely spurious reward signals.

This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on concentration of measure and careful analysis to justify the correctness and sample complexity of the procedure, our adaptive algorithm is learned via adversarial training over equivalence classes of problems derived from information theoretic lower bounds. In particular, a single adaptive learning algorithm is learned that competes with the best adaptive algorithm learned for each equivalence class. Our procedure takes as input just the available queries, set of hypotheses, loss function, and total query budget. This is in contrast to existing meta-learning work that learns an adaptive algorithm relative to an explicit, user-defined subset or prior distribution over problems which can be challenging to define and be mismatched to the instance encountered at test time. This work is particularly focused on the regime when the total query budget is very small, such as a few dozen, which is much smaller than those budgets typically considered by theoretically derived algorithms. We perform synthetic experiments to justify the stability and effectiveness of the training procedure, and then evaluate the method on tasks derived from real data including a noisy 20 Questions game and a joke recommendation task.

Large language models (LLMs) recently exhibited remarkable reasoning capabilities on solving math problems. To further improve this capability, this work proposes Learning from Mistakes (LeMa), akin to human learning processes. Consider a human student who failed to solve a math problem, he will learn from what mistake he has made and how to correct it. Mimicking this error-driven learning process, LeMa fine-tunes LLMs on mistake-correction data pairs generated by GPT-4. Specifically, we first collect inaccurate reasoning paths from various LLMs and then employ GPT-4 as a "corrector" to (1) identify the mistake step, (2) explain the reason for the mistake, and (3) correct the mistake and generate the final answer. Experimental results demonstrate the effectiveness of LeMa: across five backbone LLMs and two mathematical reasoning tasks, LeMa consistently improves the performance compared with fine-tuning on CoT data alone. Impressively, LeMa can also benefit specialized LLMs such as WizardMath and MetaMath, achieving 85.4% pass@1 accuracy on GSM8K and 27.1% on MATH. This surpasses the SOTA performance achieved by non-execution open-source models on these challenging tasks. Our code, data and models will be publicly available at https://github.com/microsoft/CodeT.

Reasoning is an essential capacity for large language models (LLMs) to address complex tasks, where the identification of process errors is vital for improving this ability. Recently, process-level reward models (PRMs) were proposed to provide step-wise rewards that facilitate reinforcement learning and data production during training and guide LLMs toward correct steps during inference, thereby improving reasoning accuracy. However, existing benchmarks of PRMs are text-based and focus on error detection, neglecting other scenarios like reasoning search. To address this gap, we introduce MPBench, a comprehensive, multi-task, multimodal benchmark designed to systematically assess the effectiveness of PRMs in diverse scenarios. MPBench employs three evaluation paradigms, each targeting a specific role of PRMs in the reasoning process: (1) Step Correctness, which assesses the correctness of each intermediate reasoning step; (2) Answer Aggregation, which aggregates multiple solutions and selects the best one; and (3) Reasoning Process Search, which guides the search for optimal reasoning steps during inference. Through these paradigms, MPBench makes comprehensive evaluations and provides insights into the development of multimodal PRMs.

We focus on a simple, one-dimensional collective decision problem (often referred to as the facility location problem) and explore issues of strategyproofness and proportionality-based fairness. We introduce and analyze a hierarchy of proportionality-based fairness axioms of varying strength: Individual Fair Share (IFS), Unanimous Fair Share (UFS), Proportionality (as in Freeman et al, 2021), and Proportional Fairness (PF). For each axiom, we characterize the family of mechanisms that satisfy the axiom and strategyproofness. We show that imposing strategyproofness renders many of the axioms to be equivalent: the family of mechanisms that satisfy proportionality, unanimity, and strategyproofness is equivalent to the family of mechanisms that satisfy UFS and strategyproofness, which, in turn, is equivalent to the family of mechanisms that satisfy PF and strategyproofness. Furthermore, there is a unique such mechanism: the Uniform Phantom mechanism, which is studied in Freeman et al. (2021). We also characterize the outcomes of the Uniform Phantom mechanism as the unique (pure) equilibrium outcome for any mechanism that satisfies continuity, strict monotonicity, and UFS. Finally, we analyze the approximation guarantees, in terms of optimal social welfare and minimum total cost, obtained by mechanisms that are strategyproof and satisfy each proportionality-based fairness axiom. We show that the Uniform Phantom mechanism provides the best approximation of the optimal social welfare (and also minimum total cost) among all mechanisms that satisfy UFS.

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes during chain-of-thought (CoT) generation, leading to severe overthinking phenomena. In response, recent studies have designed reward functions to reinforce models' behaviors in producing shorter yet correct completions. Nevertheless, we observe that these length-penalty reward functions exacerbate RL training instability: as the completion length decreases, model accuracy abruptly collapses, often occurring early in training. To address this issue, we propose a simple yet effective solution GRPO-lambda, an efficient and stabilized variant of GRPO, which dynamically adjusts the reward strategy by monitoring the correctness ratio among completions within each query-sampled group. A low correctness ratio indicates the need to avoid length penalty that compromises CoT quality, triggering a switch to length-agnostic 0/1 rewards that prioritize reasoning capability. A high ratio maintains length penalties to boost efficiency. Experimental results show that our approach avoids training instability caused by length penalty while maintaining the optimal accuracy-efficiency trade-off. On the GSM8K, GPQA, MATH-500, AMC 2023, and AIME 2024 benchmarks, it improves average accuracy by 1.48% while reducing CoT sequence length by 47.3%.

In many applications of Reinforcement Learning (RL), it is critically important that the algorithm performs safely, such that instantaneous hard constraints are satisfied at each step, and unsafe states and actions are avoided. However, existing algorithms for ''safe'' RL are often designed under constraints that either require expected cumulative costs to be bounded or assume all states are safe. Thus, such algorithms could violate instantaneous hard constraints and traverse unsafe states (and actions) in practice. Therefore, in this paper, we develop the first near-optimal safe RL algorithm for episodic Markov Decision Processes with unsafe states and actions under instantaneous hard constraints and the linear mixture model. It not only achieves a regret O(d H^3 sqrt{dK}{Delta_c}) that tightly matches the state-of-the-art regret in the setting with only unsafe actions and nearly matches that in the unconstrained setting, but is also safe at each step, where d is the feature-mapping dimension, K is the number of episodes, H is the number of steps in each episode, and Delta_c is a safety-related parameter. We also provide a lower bound Omega(max{dH K, H{Delta_c^2}}), which indicates that the dependency on Delta_c is necessary. Further, both our algorithm design and regret analysis involve several novel ideas, which may be of independent interest.

Simple regret is a natural and parameter-free performance criterion for pure exploration in multi-armed bandits yet is less popular than the probability of missing the best arm or an epsilon-good arm, perhaps due to lack of easy ways to characterize it. In this paper, we make significant progress on minimizing simple regret in both data-rich (Tge n) and data-poor regime (T le n) where n is the number of arms, and T is the number of samples. At its heart is our improved instance-dependent analysis of the well-known Sequential Halving (SH) algorithm, where we bound the probability of returning an arm whose mean reward is not within epsilon from the best (i.e., not epsilon-good) for any choice of epsilon>0, although epsilon is not an input to SH. Our bound not only leads to an optimal worst-case simple regret bound of n/T up to logarithmic factors but also essentially matches the instance-dependent lower bound for returning an epsilon-good arm reported by Katz-Samuels and Jamieson (2020). For the more challenging data-poor regime, we propose Bracketing SH (BSH) that enjoys the same improvement even without sampling each arm at least once. Our empirical study shows that BSH outperforms existing methods on real-world tasks.

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret performance compared to existing approaches. The first algorithm, although computationally inefficient, ensures a regret of mathcal{O}left(Kright), where K is the number of episodes. This is the first result with the optimal K dependence in the considered setting. The second algorithm, which is based on the policy optimization framework, guarantees a regret of mathcal{O}left(K^{3{4}} right) and is computationally efficient. Both our results significantly improve over the state-of-the-art: a computationally inefficient algorithm by Kong et al. [2023] with mathcal{O}left(K^{4{5}}+polyleft(1{lambda_{min}}right) right) regret, for some problem-dependent constant lambda_{min} that can be arbitrarily close to zero, and a computationally efficient algorithm by Sherman et al. [2023b] with mathcal{O}left(K^{6{7}} right) regret.

Large language models (LLMs) are increasingly used for tasks that require complex reasoning. Most benchmarks focus on final outcomes but overlook the intermediate reasoning steps - such as planning, revision, and decision making under resource constraints. We argue that measuring these internal processes is essential for understanding model behavior and improving reliability. We propose using strategic games as a natural evaluation environment: closed, rule-based systems with clear states, limited resources, and automatic feedback. We introduce a framework that evaluates LLMs along three core dimensions: planning, revision, and resource-constrained decision making. To operationalize this, we define metrics beyond win rate, including overcorrection risk rate, correction success rate, improvement slope, and over-budget ratio. In 4320 adversarial rounds across 12 leading models, ChatGPT-o3-mini achieves the top composite score, with a win rate of 74.7 percent, a correction success rate of 78.6 percent, and an improvement slope of 0.041. By contrast, Qwen-Plus, despite an overcorrection risk rate of 81.6 percent, wins only 25.6 percent of its matches - primarily due to excessive resource use. We also observe a negative correlation between overcorrection risk rate and correction success rate (Pearson r = -0.51, p = 0.093), suggesting that more frequent edits do not always improve outcomes. Our findings highlight the value of assessing not only what LLMs decide but how they arrive at those decisions

We consider algorithms for learning reward functions from human preferences over pairs of trajectory segments, as used in reinforcement learning from human feedback (RLHF). Most recent work assumes that human preferences are generated based only upon the reward accrued within those segments, or their partial return. Recent work casts doubt on the validity of this assumption, proposing an alternative preference model based upon regret. We investigate the consequences of assuming preferences are based upon partial return when they actually arise from regret. We argue that the learned function is an approximation of the optimal advantage function, A^*_r, not a reward function. We find that if a specific pitfall is addressed, this incorrect assumption is not particularly harmful, resulting in a highly shaped reward function. Nonetheless, this incorrect usage of A^*_r is less desirable than the appropriate and simpler approach of greedy maximization of A^*_r. From the perspective of the regret preference model, we also provide a clearer interpretation of fine tuning contemporary large language models with RLHF. This paper overall provides insight regarding why learning under the partial return preference model tends to work so well in practice, despite it conforming poorly to how humans give preferences.

Existing safety assurance research has primarily focused on training-phase alignment to instill safe behaviors into LLMs. However, recent studies have exposed these methods' susceptibility to diverse jailbreak attacks. Concurrently, inference scaling has significantly advanced LLM reasoning capabilities but remains unexplored in the context of safety assurance. Addressing this gap, our work pioneers inference scaling for robust and effective LLM safety against emerging threats. We reveal that conventional inference scaling techniques, despite their success in reasoning tasks, perform poorly in safety contexts, even falling short of basic approaches like Best-of-N Sampling. We attribute this inefficiency to a newly identified challenge, the exploration--efficiency dilemma, arising from the high computational overhead associated with frequent process reward model (PRM) evaluations. To overcome this dilemma, we propose SAFFRON, a novel inference scaling paradigm tailored explicitly for safety assurance. Central to our approach is the introduction of a multifurcation reward model (MRM) that significantly reduces the required number of reward model evaluations. To operationalize this paradigm, we further propose: (i) a partial supervision training objective for MRM, (ii) a conservative exploration constraint to prevent out-of-distribution explorations, and (iii) a Trie-based key--value caching strategy that facilitates cache sharing across sequences during tree search. Extensive experiments validate the effectiveness of our method. Additionally, we publicly release our trained multifurcation reward model (Saffron-1) and the accompanying token-level safety reward dataset (Safety4M) to accelerate future research in LLM safety. Our code, model, and data are publicly available at https://github.com/q-rz/saffron , and our project homepage is at https://q-rz.github.io/p/saffron .

The reproducibility of many experimental results in Deep Reinforcement Learning (RL) is under question. To solve this reproducibility crisis, we propose a theoretically sound methodology to compare multiple Deep RL algorithms. The performance of one execution of a Deep RL algorithm is random so that independent executions are needed to assess it precisely. When comparing several RL algorithms, a major question is how many executions must be made and how can we assure that the results of such a comparison is theoretically sound. Researchers in Deep RL often use less than 5 independent executions to compare algorithms: we claim that this is not enough in general. Moreover, when comparing several algorithms at once, the error of each comparison accumulates and must be taken into account with a multiple tests procedure to preserve low error guarantees. To address this problem in a statistically sound way, we introduce AdaStop, a new statistical test based on multiple group sequential tests. When comparing algorithms, AdaStop adapts the number of executions to stop as early as possible while ensuring that we have enough information to distinguish algorithms that perform better than the others in a statistical significant way. We prove both theoretically and empirically that AdaStop has a low probability of making an error (Family-Wise Error). Finally, we illustrate the effectiveness of AdaStop in multiple use-cases, including toy examples and difficult cases such as Mujoco environments.

Proportionality is an attractive fairness concept that has been applied to a range of problems including the facility location problem, a classic problem in social choice. In our work, we propose a concept called Strong Proportionality, which ensures that when there are two groups of agents at different locations, both groups incur the same total cost. We show that although Strong Proportionality is a well-motivated and basic axiom, there is no deterministic strategyproof mechanism satisfying the property. We then identify a randomized mechanism called Random Rank (which uniformly selects a number k between 1 to n and locates the facility at the k'th highest agent location) which satisfies Strong Proportionality in expectation. Our main theorem characterizes Random Rank as the unique mechanism that achieves universal truthfulness, universal anonymity, and Strong Proportionality in expectation among all randomized mechanisms. Finally, we show via the AverageOrRandomRank mechanism that even stronger ex-post fairness guarantees can be achieved by weakening universal truthfulness to strategyproofness in expectation.

Evaluating the step-by-step reliability of large language model (LLM) reasoning, such as Chain-of-Thought, remains challenging due to the difficulty and cost of obtaining high-quality step-level supervision. In this paper, we introduce Self-Play Critic (SPC), a novel approach where a critic model evolves its ability to assess reasoning steps through adversarial self-play games, eliminating the need for manual step-level annotation. SPC involves fine-tuning two copies of a base model to play two roles, namely a "sneaky generator" that deliberately produces erroneous steps designed to be difficult to detect, and a "critic" that analyzes the correctness of reasoning steps. These two models engage in an adversarial game in which the generator aims to fool the critic, while the critic model seeks to identify the generator's errors. Using reinforcement learning based on the game outcomes, the models iteratively improve; the winner of each confrontation receives a positive reward and the loser receives a negative reward, driving continuous self-evolution. Experiments on three reasoning process benchmarks (ProcessBench, PRM800K, DeltaBench) demonstrate that our SPC progressively enhances its error detection capabilities (e.g., accuracy increases from 70.8% to 77.7% on ProcessBench) and surpasses strong baselines, including distilled R1 model. Furthermore, applying SPC to guide the test-time search of diverse LLMs significantly improves their mathematical reasoning performance on MATH500 and AIME2024, outperforming state-of-the-art process reward models.

Recent advances have shown success in eliciting strong reasoning abilities in multimodal large language models (MLLMs) through rule-based reinforcement learning (RL) with outcome rewards. However, this paradigm typically lacks supervision over the thinking process leading to the final outcome.As a result, the model may learn sub-optimal reasoning strategies, which can hinder its generalization ability. In light of this, we propose SophiaVL-R1, as an attempt to add reward signals for the thinking process in this paradigm. To achieve this, we first train a thinking reward model that evaluates the quality of the entire thinking process. Given that the thinking reward may be unreliable for certain samples due to reward hacking, we propose the Trust-GRPO method, which assigns a trustworthiness weight to the thinking reward during training. This weight is computed based on the thinking reward comparison of responses leading to correct answers versus incorrect answers, helping to mitigate the impact of potentially unreliable thinking rewards. Moreover, we design an annealing training strategy that gradually reduces the thinking reward over time, allowing the model to rely more on the accurate rule-based outcome reward in later training stages. Experiments show that our SophiaVL-R1 surpasses a series of reasoning MLLMs on various benchmarks (e.g., MathVisita, MMMU), demonstrating strong reasoning and generalization capabilities. Notably, our SophiaVL-R1-7B even outperforms LLaVA-OneVision-72B on most benchmarks, despite the latter having 10 times more parameters. All code, models, and datasets are made publicly available at https://github.com/kxfan2002/SophiaVL-R1.

Randomized mechanisms can have good normative properties compared to their deterministic counterparts. However, randomized mechanisms are problematic in several ways such as in their verifiability. We propose here to derandomize such mechanisms by having agents play a game instead of tossing a coin. The game is designed so an agent's best action is to play randomly, and this play then injects ``randomness'' into the mechanism. This derandomization retains many of the good normative properties of the original randomized mechanism but gives a mechanism that is deterministic and easy, for instance, to audit. We consider three related methods to derandomize randomized mechanism in six different domains: voting, facility location, task allocation, school choice, peer selection, and resource allocation. We propose a number of novel derandomized mechanisms for these six domains with good normative properties. Each mechanism has a mixed Nash equilibrium in which agents play a modular arithmetic game with an uniform mixed strategy. In all but one mixed Nash equilibrium, agents report their preferences over the original problem sincerely. The derandomized methods are thus ``quasi-strategy proof''. In one domain, we additionally show that a new and desirable normative property emerges as a result of derandomization.

Recent advancements in large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, single-shot inference often yields unreliable results for complex reasoning tasks, leading researchers to explore multiple reasoning paths through methods such as perplexity and self-consistency. In this paper, we present the first theoretical error decomposition analysis of these techniques, breaking down their error into estimation error and model error. Our analysis reveals a fundamental trade-off: perplexity methods suffer from substantial model error due to the absence of a proper consistency function, while self-consistency exhibits high estimation error due to a slow error convergence rate. To overcome these limitations, we propose Reasoning-Pruning Perplexity Consistency (RPC). This approach combines Perplexity Consistency, which seamlessly integrates LLM perplexity with self-consistency, and Reasoning Pruning, which eliminates low-probability reasoning paths to effectively prevent the degeneration of estimation error reduction. Theoretical analysis demonstrates that RPC not only accelerates the convergence rate of estimation error to an exponential level but also holds strong potential for further reducing model error. Extensive empirical evaluations on seven benchmark datasets confirm that RPC can significantly improve reasoning performance, sample efficiency, and confidence reliability.

Current large-language models (LLMs) typically adopt a fixed reasoning strategy, either simple or complex, for all questions, regardless of their difficulty. This neglect of variation in task and reasoning process complexity leads to an imbalance between performance and efficiency. Existing methods attempt to implement training-free fast-slow thinking system switching to handle problems of varying difficulty, but are limited by coarse-grained solution-level strategy adjustments. To address this issue, we propose a novel reasoning paradigm: Process-Level Adaptive Thinking Mode Switching (PATS), which enables LLMs to dynamically adjust their reasoning strategy based on the difficulty of each step, optimizing the balance between accuracy and computational efficiency. Our approach integrates Process Reward Models (PRMs) with Beam Search, incorporating progressive mode switching and bad-step penalty mechanisms. Experiments on diverse mathematical benchmarks demonstrate that our methodology achieves high accuracy while maintaining moderate token usage. This study emphasizes the significance of process-level, difficulty-aware reasoning strategy adaptation, offering valuable insights into efficient inference for LLMs.

Standard federated learning (FL) approaches are vulnerable to the free-rider dilemma: participating agents can contribute little to nothing yet receive a well-trained aggregated model. While prior mechanisms attempt to solve the free-rider dilemma, none have addressed the issue of truthfulness. In practice, adversarial agents can provide false information to the server in order to cheat its way out of contributing to federated training. In an effort to make free-riding-averse federated mechanisms truthful, and consequently less prone to breaking down in practice, we propose FACT. FACT is the first federated mechanism that: (1) eliminates federated free riding by using a penalty system, (2) ensures agents provide truthful information by creating a competitive environment, and (3) encourages agent participation by offering better performance than training alone. Empirically, FACT avoids free-riding when agents are untruthful, and reduces agent loss by over 4x.

Recent years have seen considerable advancements in multi-step reasoning with Large Language Models (LLMs). The previous studies have elucidated the merits of integrating feedback or search mechanisms during model inference to improve the reasoning accuracy. The Process-Supervised Reward Model (PRM), typically furnishes LLMs with step-by-step feedback during the training phase, akin to Proximal Policy Optimization (PPO) or reject sampling. Our objective is to examine the efficacy of PRM in the inference phase to help discern the optimal solution paths for multi-step tasks such as mathematical reasoning and code generation. To this end, we propose a heuristic greedy search algorithm that employs the step-level feedback from PRM to optimize the reasoning pathways explored by LLMs. This tailored PRM demonstrated enhanced results compared to the Chain of Thought (CoT) on mathematical benchmarks like GSM8K and MATH. Additionally, to explore the versatility of our approach, we develop a novel method to automatically generate step-level reward dataset for coding tasks and observed similar improved performance in the code generation tasks. Thus highlighting the robust nature of our reward-model-based approach to inference for reasoning tasks.

Dynamic treatment regimes (DTRs) are personalized, adaptive, multi-stage treatment plans that adapt treatment decisions both to an individual's initial features and to intermediate outcomes and features at each subsequent stage, which are affected by decisions in prior stages. Examples include personalized first- and second-line treatments of chronic conditions like diabetes, cancer, and depression, which adapt to patient response to first-line treatment, disease progression, and individual characteristics. While existing literature mostly focuses on estimating the optimal DTR from offline data such as from sequentially randomized trials, we study the problem of developing the optimal DTR in an online manner, where the interaction with each individual affect both our cumulative reward and our data collection for future learning. We term this the DTR bandit problem. We propose a novel algorithm that, by carefully balancing exploration and exploitation, is guaranteed to achieve rate-optimal regret when the transition and reward models are linear. We demonstrate our algorithm and its benefits both in synthetic experiments and in a case study of adaptive treatment of major depressive disorder using real-world data.

We consider the task of evaluating policies of algorithmic resource allocation through randomized controlled trials (RCTs). Such policies are tasked with optimizing the utilization of limited intervention resources, with the goal of maximizing the benefits derived. Evaluation of such allocation policies through RCTs proves difficult, notwithstanding the scale of the trial, because the individuals' outcomes are inextricably interlinked through resource constraints controlling the policy decisions. Our key contribution is to present a new estimator leveraging our proposed novel concept, that involves retrospective reshuffling of participants across experimental arms at the end of an RCT. We identify conditions under which such reassignments are permissible and can be leveraged to construct counterfactual trials, whose outcomes can be accurately ascertained, for free. We prove theoretically that such an estimator is more accurate than common estimators based on sample means -- we show that it returns an unbiased estimate and simultaneously reduces variance. We demonstrate the value of our approach through empirical experiments on synthetic, semi-synthetic as well as real case study data and show improved estimation accuracy across the board.

In recent years, Multimodal Large Language Models (MLLMs) have been extensively utilized for multimodal reasoning tasks, including Graphical User Interface (GUI) automation. Unlike general offline multimodal tasks, GUI automation is executed in online interactive environments, necessitating step-by-step decision-making based on real-time status of the environment. This task has a lower tolerance for decision-making errors at each step, as any mistakes may cumulatively disrupt the process and potentially lead to irreversible outcomes like deletions or payments. To address these issues, we introduce a pre-operative critic mechanism that provides effective feedback prior to the actual execution, by reasoning about the potential outcome and correctness of actions. Specifically, we propose a Suggestion-aware Gradient Relative Policy Optimization (S-GRPO) strategy to construct our pre-operative critic model GUI-Critic-R1, incorporating a novel suggestion reward to enhance the reliability of the model's feedback. Furthermore, we develop a reasoning-bootstrapping based data collection pipeline to create a GUI-Critic-Train and a GUI-Critic-Test, filling existing gaps in GUI critic data. Static experiments on the GUI-Critic-Test across both mobile and web domains reveal that our GUI-Critic-R1 offers significant advantages in critic accuracy compared to current MLLMs. Dynamic evaluation on GUI automation benchmark further highlights the effectiveness and superiority of our model, as evidenced by improved success rates and operational efficiency.

We consider a combinatorial multi-armed bandit problem for maximum value reward function under maximum value and index feedback. This is a new feedback structure that lies in between commonly studied semi-bandit and full-bandit feedback structures. We propose an algorithm and provide a regret bound for problem instances with stochastic arm outcomes according to arbitrary distributions with finite supports. The regret analysis rests on considering an extended set of arms, associated with values and probabilities of arm outcomes, and applying a smoothness condition. Our algorithm achieves a O((k/Delta)log(T)) distribution-dependent and a O(T) distribution-independent regret where k is the number of arms selected in each round, Delta is a distribution-dependent reward gap and T is the horizon time. Perhaps surprisingly, the regret bound is comparable to previously-known bound under more informative semi-bandit feedback. We demonstrate the effectiveness of our algorithm through experimental results.

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

We investigate the problem of stochastic, combinatorial multi-armed bandits where the learner only has access to bandit feedback and the reward function can be non-linear. We provide a general framework for adapting discrete offline approximation algorithms into sublinear alpha-regret methods that only require bandit feedback, achieving Oleft(T^2{3}log(T)^1{3}right) expected cumulative alpha-regret dependence on the horizon T. The framework only requires the offline algorithms to be robust to small errors in function evaluation. The adaptation procedure does not even require explicit knowledge of the offline approximation algorithm -- the offline algorithm can be used as black box subroutine. To demonstrate the utility of the proposed framework, the proposed framework is applied to multiple problems in submodular maximization, adapting approximation algorithms for cardinality and for knapsack constraints. The new CMAB algorithms for knapsack constraints outperform a full-bandit method developed for the adversarial setting in experiments with real-world data.

Competitions for shareable and limited resources have long been studied with strategic agents. In reality, agents often have to learn and maximize the rewards of the resources at the same time. To design an individualized competing policy, we model the competition between agents in a novel multi-player multi-armed bandit (MPMAB) setting where players are selfish and aim to maximize their own rewards. In addition, when several players pull the same arm, we assume that these players averagely share the arms' rewards by expectation. Under this setting, we first analyze the Nash equilibrium when arms' rewards are known. Subsequently, we propose a novel SelfishMPMAB with Averaging Allocation (SMAA) approach based on the equilibrium. We theoretically demonstrate that SMAA could achieve a good regret guarantee for each player when all players follow the algorithm. Additionally, we establish that no single selfish player can significantly increase their rewards through deviation, nor can they detrimentally affect other players' rewards without incurring substantial losses for themselves. We finally validate the effectiveness of the method in extensive synthetic experiments.

Multi-turn problem solving is critical yet challenging for Large Reasoning Models (LRMs) to reflect on their reasoning and revise from feedback. Existing Reinforcement Learning (RL) methods train large reasoning models on a single-turn paradigm with verifiable rewards. However, we observe that models trained with existing RL paradigms often lose their ability to solve problems across multiple turns and struggle to revise answers based on contextual feedback, leading to repetitive responses. We ask: can LRMs learn to reflect their answers in a multi-turn context? In this work, we find that training models with multi-turn RL using only unary feedback (e.g., "Let's try again") after wrong answers can improve both single-turn performance and multi-turn reasoning. We introduce Unary Feedback as Observation (UFO) for reinforcement learning, which uses minimal yet common unary user feedback during iterative problem solving. It can be easily applied to existing single-turn RL training setups. Experimental results show that RL training with UFO keeps single-turn performance and improves multi-turn reasoning accuracy by up to 14%, enabling language models to better react to feedback in multi-turn problem solving. To further minimize the number of turns needed for a correct answer while encouraging diverse reasoning when mistakes occur, we design reward structures that guide models to produce careful and deliberate answers in each turn. Code: https://github.com/lichengliu03/unary-feedback

Sampling is ubiquitous in machine learning methodologies. Due to the growth of large datasets and model complexity, we want to learn and adapt the sampling process while training a representation. Towards achieving this grand goal, a variety of sampling techniques have been proposed. However, most of them either use a fixed sampling scheme or adjust the sampling scheme based on simple heuristics. They cannot choose the best sample for model training in different stages. Inspired by "Think, Fast and Slow" (System 1 and System 2) in cognitive science, we propose a reward-guided sampling strategy called Adaptive Sample with Reward (ASR) to tackle this challenge. To the best of our knowledge, this is the first work utilizing reinforcement learning (RL) to address the sampling problem in representation learning. Our approach optimally adjusts the sampling process to achieve optimal performance. We explore geographical relationships among samples by distance-based sampling to maximize overall cumulative reward. We apply ASR to the long-standing sampling problems in similarity-based loss functions. Empirical results in information retrieval and clustering demonstrate ASR's superb performance across different datasets. We also discuss an engrossing phenomenon which we name as "ASR gravity well" in experiments.

The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total value of the admitted items. Although optimal competitive algorithms are known for this problem, they may be fundamentally unfair, i.e., individual items may be treated inequitably in different ways. We formalize a practically-relevant notion of time fairness which effectively models a trade off between static and dynamic pricing in a motivating application such as cloud resource allocation, and show that existing algorithms perform poorly under this metric. We propose a parameterized deterministic algorithm where the parameter precisely captures the Pareto-optimal trade-off between fairness (static pricing) and competitiveness (dynamic pricing). We show that randomization is theoretically powerful enough to be simultaneously competitive and fair; however, it does not work well in experiments. To further improve the trade-off between fairness and competitiveness, we develop a nearly-optimal learning-augmented algorithm which is fair, consistent, and robust (competitive), showing substantial performance improvements in numerical experiments.

Designing reward functions for efficiently guiding reinforcement learning (RL) agents toward specific behaviors is a complex task. This is challenging since it requires the identification of reward structures that are not sparse and that avoid inadvertently inducing undesirable behaviors. Naively modifying the reward structure to offer denser and more frequent feedback can lead to unintended outcomes and promote behaviors that are not aligned with the designer's intended goal. Although potential-based reward shaping is often suggested as a remedy, we systematically investigate settings where deploying it often significantly impairs performance. To address these issues, we introduce a new framework that uses a bi-level objective to learn behavior alignment reward functions. These functions integrate auxiliary rewards reflecting a designer's heuristics and domain knowledge with the environment's primary rewards. Our approach automatically determines the most effective way to blend these types of feedback, thereby enhancing robustness against heuristic reward misspecification. Remarkably, it can also adapt an agent's policy optimization process to mitigate suboptimalities resulting from limitations and biases inherent in the underlying RL algorithms. We evaluate our method's efficacy on a diverse set of tasks, from small-scale experiments to high-dimensional control challenges. We investigate heuristic auxiliary rewards of varying quality -- some of which are beneficial and others detrimental to the learning process. Our results show that our framework offers a robust and principled way to integrate designer-specified heuristics. It not only addresses key shortcomings of existing approaches but also consistently leads to high-performing solutions, even when given misaligned or poorly-specified auxiliary reward functions.

In value-based reinforcement learning methods such as deep Q-learning, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. We show that this problem persists in an actor-critic setting and propose novel mechanisms to minimize its effects on both the actor and the critic. Our algorithm builds on Double Q-learning, by taking the minimum value between a pair of critics to limit overestimation. We draw the connection between target networks and overestimation bias, and suggest delaying policy updates to reduce per-update error and further improve performance. We evaluate our method on the suite of OpenAI gym tasks, outperforming the state of the art in every environment tested.

Large language models (LLMs) have witnessed rapid advancements, demonstrating remarkable capabilities. However, a notable vulnerability persists: LLMs often uncritically accept flawed or contradictory premises, leading to inefficient reasoning and unreliable outputs. This emphasizes the significance of possessing the Premise Critique Ability for LLMs, defined as the capacity to proactively identify and articulate errors in input premises. Most existing studies assess LLMs' reasoning ability in ideal settings, largely ignoring their vulnerabilities when faced with flawed premises. Thus, we introduce the Premise Critique Bench (PCBench), designed by incorporating four error types across three difficulty levels, paired with multi-faceted evaluation metrics. We conducted systematic evaluations of 15 representative LLMs. Our findings reveal: (1) Most models rely heavily on explicit prompts to detect errors, with limited autonomous critique; (2) Premise critique ability depends on question difficulty and error type, with direct contradictions being easier to detect than complex or procedural errors; (3) Reasoning ability does not consistently correlate with the premise critique ability; (4) Flawed premises trigger overthinking in reasoning models, markedly lengthening responses due to repeated attempts at resolving conflicts. These insights underscore the urgent need to enhance LLMs' proactive evaluation of input validity, positioning premise critique as a foundational capability for developing reliable, human-centric systems. The code is available at https://github.com/MLGroupJLU/Premise_Critique.

Reinforcement learning from human feedback (RLHF) is a standard approach for fine-tuning large language models to follow instructions. As part of this process, learned reward models are used to approximately model human preferences. However, as imperfect representations of the "true" reward, these learned reward models are susceptible to overoptimization. Gao et al. (2023) studied this phenomenon in a synthetic human feedback setup with a significantly larger "gold" reward model acting as the true reward (instead of humans) and showed that overoptimization remains a persistent problem regardless of the size of the proxy reward model and training data used. Using a similar setup, we conduct a systematic study to evaluate the efficacy of using ensemble-based conservative optimization objectives, specifically worst-case optimization (WCO) and uncertainty-weighted optimization (UWO), for mitigating reward model overoptimization when using two optimization methods: (a) best-of-n sampling (BoN) (b) proximal policy optimization (PPO). We additionally extend the setup of Gao et al. (2023) to include 25% label noise to better mirror real-world conditions. Both with and without label noise, we find that conservative optimization practically eliminates overoptimization and improves performance by up to 70% for BoN sampling. For PPO, ensemble-based conservative optimization always reduces overoptimization and outperforms single reward model optimization. Moreover, combining it with a small KL penalty successfully prevents overoptimization at no performance cost. Overall, our results demonstrate that ensemble-based conservative optimization can effectively counter overoptimization.

Intelligent agents must be generalists - showing the ability to quickly adapt and generalize to varying tasks. Within the framework of reinforcement learning (RL), model-based RL algorithms learn a task-agnostic dynamics model of the world, in principle allowing them to generalize to arbitrary rewards. However, one-step models naturally suffer from compounding errors, making them ineffective for problems with long horizons and large state spaces. In this work, we propose a novel class of models - generalized occupancy models (GOMs) - that retain the generality of model-based RL while avoiding compounding error. The key idea behind GOMs is to model the distribution of all possible long-term outcomes from a given state under the coverage of a stationary dataset, along with a policy that realizes a particular outcome from the given state. These models can then quickly be used to select the optimal action for arbitrary new tasks, without having to redo policy optimization. By directly modeling long-term outcomes, GOMs avoid compounding error while retaining generality across arbitrary reward functions. We provide a practical instantiation of GOMs using diffusion models and show its efficacy as a new class of transferable models, both theoretically and empirically across a variety of simulated robotics problems. Videos and code at https://weirdlabuw.github.io/gom/.

Reinforcement Learning with Verifiable Rewards (RLVR) demonstrates promising potential in advancing the reasoning capabilities of LLMs. However, its success remains largely confined to mathematical and code domains. This primary limitation stems from the heavy reliance on domain-specific verifiers, which results in prohibitive complexity and limited scalability. To address the challenge, our key observation is that LLM's intrinsic probability of generating a correct free-form answer directly indicates its own evaluation of the reasoning reward (i.e., how well the reasoning process leads to the correct answer). Building on this insight, we propose RLPR, a simple verifier-free framework that extrapolates RLVR to broader general domains. RLPR uses the LLM's own token probability scores for reference answers as the reward signal and maximizes the expected reward during training. We find that addressing the high variance of this noisy probability reward is crucial to make it work, and propose prob-to-reward and stabilizing methods to ensure a precise and stable reward from LLM intrinsic probabilities. Comprehensive experiments in four general-domain benchmarks and three mathematical benchmarks show that RLPR consistently improves reasoning capabilities in both areas for Gemma, Llama, and Qwen based models. Notably, RLPR outperforms concurrent VeriFree by 7.6 points on TheoremQA and 7.5 points on Minerva, and even surpasses strong verifier-model-dependent approaches General-Reasoner by 1.6 average points across seven benchmarks.

Vision-language model-based mobile agents have gained the ability to not only understand complex instructions and mobile screenshots, but also optimize their action outputs via thinking and reasoning, benefiting from reinforcement learning, such as Group Relative Policy Optimization (GRPO). However, existing research centers on offline reinforcement learning training or online optimization using action-level rewards, which limits the agent's dynamic interaction with the environment. This often results in agents settling into local optima, thereby weakening their ability for exploration and error action correction. To address these challenges, we introduce an approach called Mobile-R1, which employs interactive multi-turn reinforcement learning with task-level rewards for mobile agents. Our training framework consists of three stages: initial format finetuning, single-step online training via action-level reward, followed by online training via task-level reward based on multi-turn trajectories. This strategy is designed to enhance the exploration and error correction capabilities of Mobile-R1, leading to significant performance improvements. Moreover, we have collected a dataset covering 28 Chinese applications with 24,521 high-quality manual annotations and established a new benchmark with 500 trajectories. We will open source all resources, including the dataset, benchmark, model weight, and codes: https://mobile-r1.github.io/Mobile-R1/.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a dominant approach for aligning LLM outputs with human preferences. Inspired by the success of RLHF, we study the performance of multiple algorithms that learn from feedback (Expert Iteration, Proximal Policy Optimization (PPO), Return-Conditioned RL) on improving LLM reasoning capabilities. We investigate both sparse and dense rewards provided to the LLM both heuristically and via a learned reward model. We additionally start from multiple model sizes and initializations both with and without supervised fine-tuning (SFT) data. Overall, we find all algorithms perform comparably, with Expert Iteration performing best in most cases. Surprisingly, we find the sample complexity of Expert Iteration is similar to that of PPO, requiring at most on the order of 10^6 samples to converge from a pretrained checkpoint. We investigate why this is the case, concluding that during RL training models fail to explore significantly beyond solutions already produced by SFT models. Additionally, we discuss a trade off between maj@1 and pass@96 metric performance during SFT training and how conversely RL training improves both simultaneously. We then conclude by discussing the implications of our findings for RLHF and the future role of RL in LLM fine-tuning.

Large Reasoning Models (LRMs) have the ability to self-correct even when they make mistakes in their reasoning paths. However, our study reveals that when the reasoning process starts with a short but poor beginning, it becomes difficult for the model to recover. We refer to this phenomenon as the "Prefix Dominance Trap". Inspired by psychological findings that peer interaction can promote self-correction without negatively impacting already accurate individuals, we propose **Learning from Peers** (LeaP) to address this phenomenon. Specifically, every tokens, each reasoning path summarizes its intermediate reasoning and shares it with others through a routing mechanism, enabling paths to incorporate peer insights during inference. However, we observe that smaller models sometimes fail to follow summarization and reflection instructions effectively. To address this, we fine-tune them into our **LeaP-T** model series. Experiments on AIME 2024, AIME 2025, AIMO 2025, and GPQA Diamond show that LeaP provides substantial improvements. For instance, QwQ-32B with LeaP achieves nearly 5 absolute points higher than the baseline on average, and surpasses DeepSeek-R1-671B on three math benchmarks with an average gain of 3.3 points. Notably, our fine-tuned LeaP-T-7B matches the performance of DeepSeek-R1-Distill-Qwen-14B on AIME 2024. In-depth analysis reveals LeaP's robust error correction by timely peer insights, showing strong error tolerance and handling varied task difficulty. LeaP marks a milestone by enabling LRMs to collaborate during reasoning. Our code, datasets, and models are available at https://learning-from-peers.github.io/ .

Process Reward Models (PRMs), which provide step-by-step feedback on the reasoning generated by Large Language Models (LLMs), are receiving increasing attention. However, two key research gaps remain: collecting accurate step-level error labels for training typically requires costly human annotation, and existing PRMs are limited to math reasoning problems. In response to these gaps, this paper aims to address the challenges of automatic dataset creation and the generalization of PRMs to diverse reasoning tasks. To achieve this goal, we propose FoVer, an approach for training PRMs on step-level error labels automatically annotated by formal verification tools, such as Z3 for formal logic and Isabelle for theorem proof, which provide automatic and accurate verification for symbolic tasks. Using this approach, we synthesize a training dataset with error labels on LLM responses for formal logic and theorem proof tasks without human annotation. Although this data synthesis is feasible only for tasks compatible with formal verification, we observe that LLM-based PRMs trained on our dataset exhibit cross-task generalization, improving verification across diverse reasoning tasks. Specifically, PRMs trained with FoVer significantly outperform baseline PRMs based on the original LLMs and achieve competitive or superior results compared to state-of-the-art PRMs trained on labels annotated by humans or stronger models, as measured by step-level verification on ProcessBench and Best-of-K performance across 12 reasoning benchmarks, including MATH, AIME, ANLI, MMLU, and BBH. The datasets, models, and code are provided at https://github.com/psunlpgroup/FoVer.

When applying offline reinforcement learning (RL) in healthcare scenarios, the out-of-distribution (OOD) issues pose significant risks, as inappropriate generalization beyond clinical expertise can result in potentially harmful recommendations. While existing methods like conservative Q-learning (CQL) attempt to address the OOD issue, their effectiveness is limited by only constraining action selection by suppressing uncertain actions. This action-only regularization imitates clinician actions that prioritize short-term rewards, but it fails to regulate downstream state trajectories, thereby limiting the discovery of improved long-term treatment strategies. To safely improve policy beyond clinician recommendations while ensuring that state-action trajectories remain in-distribution, we propose Offline Guarded Safe Reinforcement Learning (OGSRL), a theoretically grounded model-based offline RL framework. OGSRL introduces a novel dual constraint mechanism for improving policy with reliability and safety. First, the OOD guardian is established to specify clinically validated regions for safe policy exploration. By constraining optimization within these regions, it enables the reliable exploration of treatment strategies that outperform clinician behavior by leveraging the full patient state history, without drifting into unsupported state-action trajectories. Second, we introduce a safety cost constraint that encodes medical knowledge about physiological safety boundaries, providing domain-specific safeguards even in areas where training data might contain potentially unsafe interventions. Notably, we provide theoretical guarantees on safety and near-optimality: policies that satisfy these constraints remain in safe and reliable regions and achieve performance close to the best possible policy supported by the data.

Existing approaches to language model alignment often treat safety as a tradeoff against helpfulness, which can lead to unacceptable responses in sensitive domains. To ensure reliable performance in such settings, we propose High-Confidence Safe Reinforcement Learning from Human Feedback (HC-RLHF), a method that provides high-confidence safety guarantees while maximizing helpfulness. Similar to previous methods, HC-RLHF explicitly decouples human preferences into helpfulness and harmlessness (safety), which are learned by training a reward model and a cost model, respectively. It then employs a two-step process to find safe solutions. In the first step, it optimizes the reward function under an intentionally pessimistic version of the cost constraint. In the second step, the trained model undergoes a safety test to verify whether its performance stays within an upper-confidence bound of the actual cost constraint. We provide a theoretical analysis of HC-RLHF, including proof that it will not return an unsafe solution with a probability greater than a user-specified threshold. For our empirical analysis, we apply HC-RLHF to align three different language models (Qwen2-1.5B, Qwen2.5-3B, and LLaMa3.2-3B) with human preferences. Our results demonstrate that HC-RLHF produces safe models with high probability and can improve harmlessness and helpfulness compared to previous methods.

Process Reward Modeling (PRM) is critical for complex reasoning and decision-making tasks where the accuracy of intermediate steps significantly influences the overall outcome. Existing PRM approaches, primarily framed as classification problems, employ cross-entropy loss to independently evaluate each step's correctness. This method can lead to suboptimal reward distribution and does not adequately address the interdependencies among steps. To address these limitations, we introduce the Process Q-value Model (PQM), a novel framework that redefines PRM in the context of a Markov Decision Process. PQM optimizes Q-value rankings based on a novel comparative loss function, enhancing the model's ability to capture the intricate dynamics among sequential decisions. This approach provides a more granular and theoretically grounded methodology for process rewards. Our extensive empirical evaluations across various sampling policies, language model backbones, and multi-step reasoning benchmarks show that PQM outperforms classification-based PRMs. The effectiveness of the comparative loss function is highlighted in our comprehensive ablation studies, confirming PQM's practical efficacy and theoretical advantage.

Model-Based Reinforcement Learning (RL) is widely believed to have the potential to improve sample efficiency by allowing an agent to synthesize large amounts of imagined experience. Experience Replay (ER) can be considered a simple kind of model, which has proved extremely effective at improving the stability and efficiency of deep RL. In principle, a learned parametric model could improve on ER by generalizing from real experience to augment the dataset with additional plausible experience. However, owing to the many design choices involved in empirically successful algorithms, it can be very hard to establish where the benefits are actually coming from. Here, we provide theoretical and empirical insight into when, and how, we can expect data generated by a learned model to be useful. First, we provide a general theorem motivating how learning a model as an intermediate step can narrow down the set of possible value functions more than learning a value function directly from data using the Bellman equation. Second, we provide an illustrative example showing empirically how a similar effect occurs in a more concrete setting with neural network function approximation. Finally, we provide extensive experiments showing the benefit of model-based learning for online RL in environments with combinatorial complexity, but factored structure that allows a learned model to generalize. In these experiments, we take care to control for other factors in order to isolate, insofar as possible, the benefit of using experience generated by a learned model relative to ER alone.

Process Reward Models (PRMs) emerge as a promising approach for process supervision in mathematical reasoning of Large Language Models (LLMs), which aim to identify and mitigate intermediate errors in the reasoning processes. However, the development of effective PRMs faces significant challenges, particularly in data annotation and evaluation methodologies. In this paper, through extensive experiments, we demonstrate that commonly used Monte Carlo (MC) estimation-based data synthesis for PRMs typically yields inferior performance and generalization compared to LLM-as-a-judge and human annotation methods. MC estimation relies on completion models to evaluate current-step correctness, leading to inaccurate step verification. Furthermore, we identify potential biases in conventional Best-of-N (BoN) evaluation strategies for PRMs: (1) The unreliable policy models generate responses with correct answers but flawed processes, leading to a misalignment between the evaluation criteria of BoN and the PRM objectives of process verification. (2) The tolerance of PRMs of such responses leads to inflated BoN scores. (3) Existing PRMs have a significant proportion of minimum scores concentrated on the final answer steps, revealing the shift from process to outcome-based assessment in BoN Optimized PRMs. To address these challenges, we develop a consensus filtering mechanism that effectively integrates MC estimation with LLM-as-a-judge and advocates a more comprehensive evaluation framework that combines response-level and step-level metrics. Based on the mechanisms, we significantly improve both model performance and data efficiency in the BoN evaluation and the step-wise error identification task. Finally, we release a new state-of-the-art PRM that outperforms existing open-source alternatives and provides practical guidelines for future research in building process supervision models.

Recent advances in large reasoning models highlight Reinforcement Learning with Verifiable Rewards (RLVR) as a promising method for enhancing AI's capabilities, particularly in solving complex logical tasks. However, it remains unclear whether RLVR truly expands a model's reasoning boundary or merely amplifies high-reward outputs that the base model already knows for improved precision. This study presents a theoretical and empirical investigation that provides fresh insights into the potential limits of RLVR. First, we offer a new theoretical perspective that RLVR is constrained by the base model's support-unable to sample solutions with zero initial probability-and operates as a conservative reweighting mechanism that may restrict the discovery of entirely original solutions. We also identify an entropy-reward tradeoff: while RLVR reliably enhances precision, it may progressively narrow exploration and potentially overlook correct yet underrepresented solutions. Extensive empirical experiments validate that while RLVR consistently improves pass@1, the shrinkage of empirical support generally outweighs the expansion of empirical support under larger sampling budgets, failing to recover correct answers that were previously accessible to the base model. Interestingly, we also observe that while RLVR sometimes increases token-level entropy, resulting in greater uncertainty at each generation step, answer-level entropy declines, indicating that these seemingly more uncertain paths ultimately converge onto a smaller set of distinct answers. Taken together, these findings reveal potential limits of RLVR in extending reasoning horizons. Breaking this invisible leash may require future algorithmic innovations such as explicit exploration mechanisms or hybrid strategies that seed probability mass into underrepresented solution regions.

In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance tau. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is Omega(tau^{-1AK}), where A is the number of actions and K is the number of episodes, and that it is achieved by an Upper Confidence Bound algorithm with a novel Bernstein bonus. For online RL in tabular Markov Decision Processes (MDPs), we show a minimax regret lower bound of Omega(tau^{-1SAK}) (with normalized cumulative rewards), where S is the number of states, and we propose a novel bonus-driven Value Iteration procedure. We show that our algorithm achieves the optimal regret of widetilde O(tau^{-1SAK}) under a continuity assumption and in general attains a near-optimal regret of widetilde O(tau^{-1}SAK), which is minimax-optimal for constant tau. This improves on the best available bounds. By discretizing rewards appropriately, our algorithms are computationally efficient.

Reasoning methods that adaptively allocate test-time compute have advanced LLM performance on easy to verify domains such as math and code. In this work, we study how to utilize this approach to train models that exhibit a degree of robustness to safety vulnerabilities, and show that doing so can provide benefits. We build a recipe called TARS (Training Adaptive Reasoners for Safety), a reinforcement learning (RL) approach that trains models to reason about safety using chain-of-thought traces and a reward signal that balances safety with task completion. To build TARS, we identify three critical design choices: (1) a "lightweight" warmstart SFT stage, (2) a mix of harmful, harmless, and ambiguous prompts to prevent shortcut behaviors such as too many refusals, and (3) a reward function to prevent degeneration of reasoning capabilities during training. Models trained with TARS exhibit adaptive behaviors by spending more compute on ambiguous queries, leading to better safety-refusal trade-offs. They also internally learn to better distinguish between safe and unsafe prompts and attain greater robustness to both white-box (e.g., GCG) and black-box attacks (e.g., PAIR). Overall, our work provides an effective, open recipe for training LLMs against jailbreaks and harmful requests by reasoning per prompt.

Multi-agent systems commonly distribute tasks among specialized, autonomous agents, yet they often lack mechanisms to replace or reassign underperforming agents in real time. Inspired by the free-agency model of Major League Baseball, the Reinforcement Learning Free Agent (RLFA) algorithm introduces a reward-based mechanism to detect and remove agents exhibiting persistent underperformance and seamlessly insert more capable ones. Each agent internally uses a mixture-of-experts (MoE) approach, delegating incoming tasks to specialized sub-models under the guidance of a gating function. A primary use case is fraud detection, where RLFA promptly swaps out an agent whose detection accuracy dips below a preset threshold. A new agent is tested in a probationary mode, and upon demonstrating superior performance, fully replaces the underperformer. This dynamic, free-agency cycle ensures sustained accuracy, quicker adaptation to emerging threats, and minimal disruption to ongoing operations. By continually refreshing its roster of agents, the system fosters ongoing improvements and more resilient collaboration in multi-agent Generative AI environments.

We study principal-agent problems in which a principal commits to an outcome-dependent payment scheme -- called contract -- in order to induce an agent to take a costly, unobservable action leading to favorable outcomes. We consider a generalization of the classical (single-round) version of the problem in which the principal interacts with the agent by committing to contracts over multiple rounds. The principal has no information about the agent, and they have to learn an optimal contract by only observing the outcome realized at each round. We focus on settings in which the size of the agent's action space is small. We design an algorithm that learns an approximately-optimal contract with high probability in a number of rounds polynomial in the size of the outcome space, when the number of actions is constant. Our algorithm solves an open problem by Zhu et al.[2022]. Moreover, it can also be employed to provide a mathcal{O}(T^{4/5}) regret bound in the related online learning setting in which the principal aims at maximizing their cumulative utility, thus considerably improving previously-known regret bounds.

Recent work has shown that asking language models to generate reasoning steps improves performance on many reasoning tasks. When moving beyond prompting, this raises the question of how we should supervise such models: outcome-based approaches which supervise the final result, or process-based approaches which supervise the reasoning process itself? Differences between these approaches might naturally be expected not just in final-answer errors but also in reasoning errors, which can be difficult to detect and are problematic in many real-world domains such as education. We run the first comprehensive comparison between process- and outcome-based approaches trained on a natural language task, GSM8K. We find that pure outcome-based supervision produces similar final-answer error rates with less label supervision. However, for correct reasoning steps we find it necessary to use process-based supervision or supervision from learned reward models that emulate process-based feedback. In total, we improve the previous best results from 16.8% to 12.7% final-answer error and 14.0% to 3.4% reasoning error among final-answer-correct solutions.

Large Language Models have achieved remarkable success in natural language processing tasks, with Reinforcement Learning playing a key role in adapting them to specific applications. However, obtaining ground truth answers for training LLMs in mathematical problem-solving is often challenging, costly, and sometimes unfeasible. This research delves into the utilization of format and length as surrogate signals to train LLMs for mathematical problem-solving, bypassing the need for traditional ground truth answers.Our study shows that a reward function centered on format correctness alone can yield performance improvements comparable to the standard GRPO algorithm in early phases. Recognizing the limitations of format-only rewards in the later phases, we incorporate length-based rewards. The resulting GRPO approach, leveraging format-length surrogate signals, not only matches but surpasses the performance of the standard GRPO algorithm relying on ground truth answers in certain scenarios, achieving 40.0\% accuracy on AIME2024 with a 7B base model. Through systematic exploration and experimentation, this research not only offers a practical solution for training LLMs to solve mathematical problems and reducing the dependence on extensive ground truth data collection, but also reveals the essence of why our label-free approach succeeds: base model is like an excellent student who has already mastered mathematical and logical reasoning skills, but performs poorly on the test paper, it simply needs to develop good answering habits to achieve outstanding results in exams , in other words, to unlock the capabilities it already possesses.

We study the problem of adaptively identifying patient subpopulations that benefit from a given treatment during a confirmatory clinical trial. This type of adaptive clinical trial has been thoroughly studied in biostatistics, but has been allowed only limited adaptivity so far. Here, we aim to relax classical restrictions on such designs and investigate how to incorporate ideas from the recent machine learning literature on adaptive and online experimentation to make trials more flexible and efficient. We find that the unique characteristics of the subpopulation selection problem -- most importantly that (i) one is usually interested in finding subpopulations with any treatment benefit (and not necessarily the single subgroup with largest effect) given a limited budget and that (ii) effectiveness only has to be demonstrated across the subpopulation on average -- give rise to interesting challenges and new desiderata when designing algorithmic solutions. Building on these findings, we propose AdaGGI and AdaGCPI, two meta-algorithms for subpopulation construction. We empirically investigate their performance across a range of simulation scenarios and derive insights into their (dis)advantages across different settings.

In reinforcement learning from human feedback, it is common to optimize against a reward model trained to predict human preferences. Because the reward model is an imperfect proxy, optimizing its value too much can hinder ground truth performance, in accordance with Goodhart's law. This effect has been frequently observed, but not carefully measured due to the expense of collecting human preference data. In this work, we use a synthetic setup in which a fixed "gold-standard" reward model plays the role of humans, providing labels used to train a proxy reward model. We study how the gold reward model score changes as we optimize against the proxy reward model using either reinforcement learning or best-of-n sampling. We find that this relationship follows a different functional form depending on the method of optimization, and that in both cases its coefficients scale smoothly with the number of reward model parameters. We also study the effect on this relationship of the size of the reward model dataset, the number of reward model and policy parameters, and the coefficient of the KL penalty added to the reward in the reinforcement learning setup. We explore the implications of these empirical results for theoretical considerations in AI alignment.

We study the non-stationary dueling bandits problem with K arms, where the time horizon T consists of M stationary segments, each of which is associated with its own preference matrix. The learner repeatedly selects a pair of arms and observes a binary preference between them as feedback. To minimize the accumulated regret, the learner needs to pick the Condorcet winner of each stationary segment as often as possible, despite preference matrices and segment lengths being unknown. We propose the Beat, the, Winner, Reset algorithm and prove a bound on its expected binary weak regret in the stationary case, which tightens the bound of current state-of-art algorithms. We also show a regret bound for the non-stationary case, without requiring knowledge of M or T. We further propose and analyze two meta-algorithms, DETECT for weak regret and Monitored, Dueling, Bandits for strong regret, both based on a detection-window approach that can incorporate any dueling bandit algorithm as a black-box algorithm. Finally, we prove a worst-case lower bound for expected weak regret in the non-stationary case.

Large Language Models (LLMs) are being increasingly used in software engineering tasks, with an increased focus on bug report resolution over the past year. However, most proposed systems fail to properly handle uncertain or incorrect inputs and outputs. Existing LLM-based tools and coding agents respond to every issue and generate a patch for every case, even when the input is vague or their own output is incorrect. There are no mechanisms in place to abstain when confidence is low. This leads to unreliable behaviour, such as hallucinated code changes or responses based on vague issue reports. We introduce BouncerBench, a benchmark that evaluates whether LLM-based software agents can refuse to act when inputs are ill-defined or refuse to respond when their own outputs are likely to be incorrect. Unlike prior benchmarks that implicitly incentivize models to generate responses even when uncertain, BouncerBench aims to improve precision by targeting two overlooked failure points: (1) vague or underspecified issue descriptions in tickets and (2) logically or functionally incorrect code patches created by the system. It measures whether proposed systems can distinguish actionable issues from vague tickets and valid patches from untrustworthy ones. We also implement a basic input and output bouncer, evaluating how well current LLMs can abstain when needed. Our results show that most models fail to abstain from underspecified inputs or incorrect outputs. Hence, we conclude that there is significant room for improvement before LLMs can be trusted to make correct decisions and recommendations in real-world software engineering workflows. BouncerBench provides a first step toward evaluating and building more cautious, trustworthy code agents. The replication package, dataset, and leaderboard can be found at bouncerbench.com

Cascades are a classical strategy to enable inference cost to vary adaptively across samples, wherein a sequence of classifiers are invoked in turn. A deferral rule determines whether to invoke the next classifier in the sequence, or to terminate prediction. One simple deferral rule employs the confidence of the current classifier, e.g., based on the maximum predicted softmax probability. Despite being oblivious to the structure of the cascade -- e.g., not modelling the errors of downstream models -- such confidence-based deferral often works remarkably well in practice. In this paper, we seek to better understand the conditions under which confidence-based deferral may fail, and when alternate deferral strategies can perform better. We first present a theoretical characterisation of the optimal deferral rule, which precisely characterises settings under which confidence-based deferral may suffer. We then study post-hoc deferral mechanisms, and demonstrate they can significantly improve upon confidence-based deferral in settings where (i) downstream models are specialists that only work well on a subset of inputs, (ii) samples are subject to label noise, and (iii) there is distribution shift between the train and test set.

In order to solve a task using reinforcement learning, it is necessary to first formalise the goal of that task as a reward function. However, for many real-world tasks, it is very difficult to manually specify a reward function that never incentivises undesirable behaviour. As a result, it is increasingly popular to use reward learning algorithms, which attempt to learn a reward function from data. However, the theoretical foundations of reward learning are not yet well-developed. In particular, it is typically not known when a given reward learning algorithm with high probability will learn a reward function that is safe to optimise. This means that reward learning algorithms generally must be evaluated empirically, which is expensive, and that their failure modes are difficult to anticipate in advance. One of the roadblocks to deriving better theoretical guarantees is the lack of good methods for quantifying the difference between reward functions. In this paper we provide a solution to this problem, in the form of a class of pseudometrics on the space of all reward functions that we call STARC (STAndardised Reward Comparison) metrics. We show that STARC metrics induce both an upper and a lower bound on worst-case regret, which implies that our metrics are tight, and that any metric with the same properties must be bilipschitz equivalent to ours. Moreover, we also identify a number of issues with reward metrics proposed by earlier works. Finally, we evaluate our metrics empirically, to demonstrate their practical efficacy. STARC metrics can be used to make both theoretical and empirical analysis of reward learning algorithms both easier and more principled.

In this paper, we present empirical evidence of skills and directed exploration emerging from a simple RL algorithm long before any successful trials are observed. For example, in a manipulation task, the agent is given a single observation of the goal state and learns skills, first for moving its end-effector, then for pushing the block, and finally for picking up and placing the block. These skills emerge before the agent has ever successfully placed the block at the goal location and without the aid of any reward functions, demonstrations, or manually-specified distance metrics. Once the agent has learned to reach the goal state reliably, exploration is reduced. Implementing our method involves a simple modification of prior work and does not require density estimates, ensembles, or any additional hyperparameters. Intuitively, the proposed method seems like it should be terrible at exploration, and we lack a clear theoretical understanding of why it works so effectively, though our experiments provide some hints.

As Large Language Models (LLMs) continue to progress toward more advanced forms of intelligence, Reinforcement Learning from Human Feedback (RLHF) is increasingly seen as a key pathway toward achieving Artificial General Intelligence (AGI). However, the reliance on reward-model-based (RM-based) alignment methods introduces significant challenges due to the inherent instability and imperfections of Reward Models (RMs), which can lead to critical issues such as reward hacking and misalignment with human intentions. In this paper, we introduce a reward-robust RLHF framework aimed at addressing these fundamental challenges, paving the way for more reliable and resilient learning in LLMs. Our approach introduces a novel optimization objective that carefully balances performance and robustness by incorporating Bayesian Reward Model Ensembles (BRME) to model the uncertainty set of reward functions. This allows the framework to integrate both nominal performance and minimum reward signals, ensuring more stable learning even with imperfect reward models. Empirical results demonstrate that our framework consistently outperforms traditional RLHF across diverse benchmarks, showing improved accuracy and long-term stability. We also provide a theoretical analysis, demonstrating that reward-robust RLHF approaches the stability of constant reward settings, which proves to be effective in a stochastic-case analysis. Together, these contributions highlight the framework potential to enhance both the performance and stability of LLM alignment with RLHF.

Given a (machine learning) classifier and a collection of unlabeled data, how can we efficiently identify misclassification patterns presented in this dataset? To address this problem, we propose a human-machine collaborative framework that consists of a team of human annotators and a sequential recommendation algorithm. The recommendation algorithm is conceptualized as a stochastic sampler that, in each round, queries the annotators a subset of samples for their true labels and obtains the feedback information on whether the samples are misclassified. The sampling mechanism needs to balance between discovering new patterns of misclassification (exploration) and confirming the potential patterns of classification (exploitation). We construct a determinantal point process, whose intensity balances the exploration-exploitation trade-off through the weighted update of the posterior at each round to form the generator of the stochastic sampler. The numerical results empirically demonstrate the competitive performance of our framework on multiple datasets at various signal-to-noise ratios.

In this paper, we introduce a novel predict-and-optimize method for profit-driven churn prevention. We frame the task of targeting customers for a retention campaign as a regret minimization problem. The main objective is to leverage individual customer lifetime values (CLVs) to ensure that only the most valuable customers are targeted. In contrast, many profit-driven strategies focus on churn probabilities while considering average CLVs. This often results in significant information loss due to data aggregation. Our proposed model aligns with the guidelines of Predict-and-Optimize (PnO) frameworks and can be efficiently solved using stochastic gradient descent methods. Results from 12 churn prediction datasets underscore the effectiveness of our approach, which achieves the best average performance compared to other well-established strategies in terms of average profit.

Uniform random exploration in decision-making systems supports off-policy learning via supervision but incurs high regret, making it impractical for many applications. Conversely, non-uniform exploration offers better immediate performance but lacks support for off-policy learning. Recent research suggests that regression oracles can bridge this gap by combining non-uniform exploration with supervised learning. In this paper, we analyze these approaches within a real-world industrial context at Adyen, a large global payments processor characterized by batch logged delayed feedback, short-term memory, and dynamic action spaces under the Empirical Risk Minimization (ERM) framework. Our analysis reveals that while regression oracles significantly improve performance, they introduce challenges due to rigid algorithmic assumptions. Specifically, we observe that as a policy improves, subsequent generations may perform worse due to shifts in the reward distribution and increased class imbalance in the training data. This degradation occurs de spite improvements in other aspects of the training data, leading to decreased performance in successive policy iterations. We further explore the long-term impact of regression oracles, identifying a potential "oscillation effect." This effect arises when regression oracles influence probability estimates and the realizability of subsequent policy models, leading to fluctuations in performance across iterations. Our findings highlight the need for more adaptable algorithms that can leverage the benefits of regression oracles without introducing instability in policy performance over time.

Machine learning models can make critical errors that are easily hidden within vast amounts of data. Such errors often run counter to rules based on human intuition. However, rules based on human knowledge are challenging to scale or to even formalize. We thereby seek to infer statistical rules from the data and quantify the extent to which a model has learned them. We propose a framework SQRL that integrates logic-based methods with statistical inference to derive these rules from a model's training data without supervision. We further show how to adapt models at test time to reduce rule violations and produce more coherent predictions. SQRL generates up to 300K rules over datasets from vision, tabular, and language settings. We uncover up to 158K violations of those rules by state-of-the-art models for classification, object detection, and data imputation. Test-time adaptation reduces these violations by up to 68.7% with relative performance improvement up to 32%. SQRL is available at https://github.com/DebugML/sqrl.

Recent advancements in large language models (LLMs) have substantially enhanced their mathematical reasoning abilities. However, these models still struggle with complex problems that require multiple reasoning steps, frequently leading to logical or numerical errors. While numerical mistakes can be largely addressed by integrating a code interpreter, identifying logical errors within intermediate steps is more challenging. Moreover, manually annotating these steps for training is not only expensive but also labor-intensive, requiring the expertise of professional annotators. In our study, we introduce an innovative approach that bypasses the need for process annotations (from human or GPTs) by utilizing the Monte Carlo Tree Search (MCTS) framework. This technique automatically generates both the process supervision and the step-level evaluation signals. Our method iteratively trains the policy and value models, leveraging the capabilities of a well-pretrained LLM to progressively enhance its mathematical reasoning skills. Furthermore, we propose an efficient inference strategy-step-level beam search, where the value model is crafted to assist the policy model (i.e., LLM) in navigating more effective reasoning paths, rather than solely relying on prior probabilities. The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.

We study self-rewarding reasoning large language models (LLMs), which can simultaneously generate step-by-step reasoning and evaluate the correctness of their outputs during the inference time-without external feedback. This integrated approach allows a single model to independently guide its reasoning process, offering computational advantages for model deployment. We particularly focus on the representative task of self-correction, where models autonomously detect errors in their responses, revise outputs, and decide when to terminate iterative refinement loops. To enable this, we propose a two-staged algorithmic framework for constructing self-rewarding reasoning models using only self-generated data. In the first stage, we employ sequential rejection sampling to synthesize long chain-of-thought trajectories that incorporate both self-rewarding and self-correction mechanisms. Fine-tuning models on these curated data allows them to learn the patterns of self-rewarding and self-correction. In the second stage, we further enhance the models' ability to assess response accuracy and refine outputs through reinforcement learning with rule-based signals. Experiments with Llama-3 and Qwen-2.5 demonstrate that our approach surpasses intrinsic self-correction capabilities and achieves performance comparable to systems that rely on external reward models.

Reinforcement learning (RL) solves sequential decision-making problems via a trial-and-error process interacting with the environment. While RL achieves outstanding success in playing complex video games that allow huge trial-and-error, making errors is always undesired in the real world. To improve the sample efficiency and thus reduce the errors, model-based reinforcement learning (MBRL) is believed to be a promising direction, which builds environment models in which the trial-and-errors can take place without real costs. In this survey, we take a review of MBRL with a focus on the recent progress in deep RL. For non-tabular environments, there is always a generalization error between the learned environment model and the real environment. As such, it is of great importance to analyze the discrepancy between policy training in the environment model and that in the real environment, which in turn guides the algorithm design for better model learning, model usage, and policy training. Besides, we also discuss the recent advances of model-based techniques in other forms of RL, including offline RL, goal-conditioned RL, multi-agent RL, and meta-RL. Moreover, we discuss the applicability and advantages of MBRL in real-world tasks. Finally, we end this survey by discussing the promising prospects for the future development of MBRL. We think that MBRL has great potential and advantages in real-world applications that were overlooked, and we hope this survey could attract more research on MBRL.

We consider the obnoxious facility location problem (in which agents prefer the facility location to be far from them) and propose a hierarchy of distance-based proportional fairness concepts for the problem. These fairness axioms ensure that groups of agents at the same location are guaranteed to be a distance from the facility proportional to their group size. We consider deterministic and randomized mechanisms, and compute tight bounds on the price of proportional fairness. In the deterministic setting, we show that our proportional fairness axioms are incompatible with strategyproofness, and prove asymptotically tight epsilon-price of anarchy and stability bounds for proportionally fair welfare-optimal mechanisms. In the randomized setting, we identify proportionally fair and strategyproof mechanisms that give an expected welfare within a constant factor of the optimal welfare. Finally, we prove existence results for two extensions to our model.

We develop a Multi-Agent Reinforcement Learning (MARL) method to learn scalable control policies for target tracking. Our method can handle an arbitrary number of pursuers and targets; we show results for tasks consisting up to 1000 pursuers tracking 1000 targets. We use a decentralized, partially-observable Markov Decision Process framework to model pursuers as agents receiving partial observations (range and bearing) about targets which move using fixed, unknown policies. An attention mechanism is used to parameterize the value function of the agents; this mechanism allows us to handle an arbitrary number of targets. Entropy-regularized off-policy RL methods are used to train a stochastic policy, and we discuss how it enables a hedging behavior between pursuers that leads to a weak form of cooperation in spite of completely decentralized control execution. We further develop a masking heuristic that allows training on smaller problems with few pursuers-targets and execution on much larger problems. Thorough simulation experiments, ablation studies, and comparisons to state of the art algorithms are performed to study the scalability of the approach and robustness of performance to varying numbers of agents and targets.

Randomized controlled trials are susceptible to imbalance on covariates predictive of the outcome. Rerandomization and deterministic treatment assignment are two proposed solutions. This paper explores the relationship between rerandomization and deterministic assignment, showing how deterministic assignment is an extreme case of rerandomization. The paper argues that in small experiments, both fully randomized and fully deterministic assignment have limitations. Instead, the researcher should consider setting the rerandomization acceptance probability based on an analysis of covariates and assumptions about the data structure to achieve an optimal alignment between randomness and balance. This allows for the calculation of minimum p-values along with valid permutation tests and fiducial intervals. The paper also introduces tools, including a new, open-source R package named fastrerandomize, to implement rerandomization and explore options for optimal rerandomization acceptance thresholds.

Large Language Models (LLMs) have exhibited strong mathematical reasoning and computational prowess, tackling tasks ranging from basic arithmetic to advanced competition-level problems. However, frequently occurring subtle errors, such as miscalculations or incorrect substitutions, limit the models' full mathematical potential. Existing studies to improve mathematical ability typically involve distilling reasoning skills from stronger LLMs or applying preference learning to step-wise response pairs. Although these methods leverage samples of varying granularity to mitigate reasoning errors, they overlook the frequently occurring subtle errors. A major reason is that sampled preference pairs involve differences unrelated to the errors, which may distract the model from focusing on subtle errors. In this work, we propose a novel preference learning framework called eRror-Injected Self-Editing (RISE), which injects predefined subtle errors into partial tokens of correct solutions to construct hard pairs for error mitigation. In detail, RISE uses the model itself to edit a small number of tokens in the solution, injecting designed subtle errors. Then, pairs composed of self-edited solutions and their corresponding correct ones, along with pairs of correct and incorrect solutions obtained through sampling, are used together for subtle error-aware DPO training. Compared with other preference learning methods, RISE further refines the training objective to focus on predefined errors and their tokens, without requiring fine-grained sampling or preference annotation. Extensive experiments validate the effectiveness of RISE, with preference learning on Qwen2-7B-Instruct yielding notable improvements of 3.0% on GSM8K and 7.9% on MATH.

We propose a general two-stage algorithm that enjoys a provable scaling law for the test-time compute of large language models (LLMs). Given an input problem, the proposed algorithm first generates N candidate solutions, and then chooses the best one via a multiple-round knockout tournament where each pair of candidates are compared for K times and only the winners move on to the next round. In a minimalistic implementation, both stages can be executed with a black-box LLM alone and nothing else (e.g., no external verifier or reward model), and a total of N times (K + 1) highly parallelizable LLM calls are needed for solving an input problem. Assuming that a generated candidate solution is correct with probability p_{gen} > 0 and a comparison between a pair of correct and incorrect solutions identifies the right winner with probability p_{comp} > 0.5 (i.e., better than a random guess), we prove theoretically that the failure probability of the proposed algorithm decays to zero exponentially with respect to N and K: $P(final output is incorrect) le (1 - p_{gen})^N + lceil log_2 N rceil e^{-2 K (p_{comp} - 0.5)^2}.$ Our empirical results with the challenging MMLU-Pro benchmark validate the technical assumptions, as well as the efficacy of the proposed algorithm and the gains from scaling up its test-time compute.

In this paper, we propose DuaShepherd, a novel reward modeling framework that integrates two complementary reward signals, correctness and potential, to enhance the mathematical reasoning capabilities of Large Language Models (LLMs). While correctness-based signals emphasize identification of stepwise errors, potential-based signals focus on the likelihood of reaching the correct final answer. We developed an automated pipeline for constructing large-scale reward modeling dataset with both signals. A unified, multi-head architecture was explored to train the two reward models in a multi-task setup, demonstrating benefits from learning both correctness and potential in parallel. By combining these two signals into a compound probability, our model achieves consistent performance improvements across multiple benchmarks. Empirical evaluations on MATH500 and ProcessBench confirm that this combined reward significantly outperforms models trained on either reward type alone, achieving state-of-the-art performance under comparable resource constraints.

Self-correction has demonstrated potential in code generation by allowing language models to revise and improve their outputs through successive refinement. Recent studies have explored prompting-based strategies that incorporate verification or feedback loops using proprietary models, as well as training-based methods that leverage their strong reasoning capabilities. However, whether smaller models possess the capacity to effectively guide their outputs through self-reflection remains unexplored. Our findings reveal that smaller models struggle to exhibit reflective revision behavior across both self-correction paradigms. In response, we introduce CoCoS, an approach designed to enhance the ability of small language models for multi-turn code correction. Specifically, we propose an online reinforcement learning objective that trains the model to confidently maintain correct outputs while progressively correcting incorrect outputs as turns proceed. Our approach features an accumulated reward function that aggregates rewards across the entire trajectory and a fine-grained reward better suited to multi-turn correction scenarios. This facilitates the model in enhancing initial response quality while achieving substantial improvements through self-correction. With 1B-scale models, CoCoS achieves improvements of 35.8% on the MBPP and 27.7% on HumanEval compared to the baselines.

Current approaches for training Process Reward Models (PRMs) often involve breaking down responses into multiple reasoning steps using rule-based techniques, such as using predefined placeholder tokens or setting the reasoning step's length into a fixed size. These approaches overlook the fact that specific words do not typically mark true decision points in a text. To address this, we propose AdaptiveStep, a method that divides reasoning steps based on the model's confidence in predicting the next word. This division method provides more decision-making information at each step, enhancing downstream tasks, such as reward model learning. Moreover, our method does not require manual annotation. We demonstrate its effectiveness through experiments with AdaptiveStep-trained PRMs in mathematical reasoning and code generation tasks. Experimental results indicate that the outcome PRM achieves state-of-the-art Best-of-N performance, surpassing greedy search strategy with token-level value-guided decoding, while also reducing construction costs by over 30% compared to existing open-source PRMs. In addition, we provide a thorough analysis and case study on the PRM's performance, transferability, and generalization capabilities.

Large Language Models (LLMs) have shown significant potential in designing reward functions for Reinforcement Learning (RL) tasks. However, obtaining high-quality reward code often involves human intervention, numerous LLM queries, or repetitive RL training. To address these issues, we propose CARD, a LLM-driven Reward Design framework that iteratively generates and improves reward function code. Specifically, CARD includes a Coder that generates and verifies the code, while a Evaluator provides dynamic feedback to guide the Coder in improving the code, eliminating the need for human feedback. In addition to process feedback and trajectory feedback, we introduce Trajectory Preference Evaluation (TPE), which evaluates the current reward function based on trajectory preferences. If the code fails the TPE, the Evaluator provides preference feedback, avoiding RL training at every iteration and making the reward function better aligned with the task objective. Empirical results on Meta-World and ManiSkill2 demonstrate that our method achieves an effective balance between task performance and token efficiency, outperforming or matching the baselines across all tasks. On 10 out of 12 tasks, CARD shows better or comparable performance to policies trained with expert-designed rewards, and our method even surpasses the oracle on 3 tasks.

We introduce ALaRM, the first framework modeling hierarchical rewards in reinforcement learning from human feedback (RLHF), which is designed to enhance the alignment of large language models (LLMs) with human preferences. The framework addresses the limitations of current alignment approaches, which often struggle with the inconsistency and sparsity of human supervision signals, by integrating holistic rewards with aspect-specific rewards. This integration enables more precise and consistent guidance of language models towards desired outcomes, particularly in complex and open text generation tasks. By employing a methodology that filters and combines multiple rewards based on their consistency, the framework provides a reliable mechanism for improving model alignment. We validate our approach through applications in long-form question answering and machine translation tasks, employing gpt-3.5-turbo for pairwise comparisons, and demonstrate improvements over existing baselines. Our work underscores the effectiveness of hierarchical rewards modeling in refining LLM training processes for better human preference alignment. We release our code at https://ALaRM-fdu.github.io.

We consider a resource-aware variant of the classical multi-armed bandit problem: In each round, the learner selects an arm and determines a resource limit. It then observes a corresponding (random) reward, provided the (random) amount of consumed resources remains below the limit. Otherwise, the observation is censored, i.e., no reward is obtained. For this problem setting, we introduce a measure of regret, which incorporates the actual amount of allocated resources of each learning round as well as the optimality of realizable rewards. Thus, to minimize regret, the learner needs to set a resource limit and choose an arm in such a way that the chance to realize a high reward within the predefined resource limit is high, while the resource limit itself should be kept as low as possible. We propose a UCB-inspired online learning algorithm, which we analyze theoretically in terms of its regret upper bound. In a simulation study, we show that our learning algorithm outperforms straightforward extensions of standard multi-armed bandit algorithms.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

Shojaee et al. (2025) report that Large Reasoning Models (LRMs) exhibit "accuracy collapse" on planning puzzles beyond certain complexity thresholds. We demonstrate that their findings primarily reflect experimental design limitations rather than fundamental reasoning failures. Our analysis reveals three critical issues: (1) Tower of Hanoi experiments systematically exceed model output token limits at reported failure points, with models explicitly acknowledging these constraints in their outputs; (2) The authors' automated evaluation framework fails to distinguish between reasoning failures and practical constraints, leading to misclassification of model capabilities; (3) Most concerningly, their River Crossing benchmarks include mathematically impossible instances for N > 5 due to insufficient boat capacity, yet models are scored as failures for not solving these unsolvable problems. When we control for these experimental artifacts, by requesting generating functions instead of exhaustive move lists, preliminary experiments across multiple models indicate high accuracy on Tower of Hanoi instances previously reported as complete failures. These findings highlight the importance of careful experimental design when evaluating AI reasoning capabilities.

The emergence of pre-trained AI systems with powerful capabilities across a diverse and ever-increasing set of complex domains has raised a critical challenge for AI safety as tasks can become too complicated for humans to judge directly. Irving et al. [2018] proposed a debate method in this direction with the goal of pitting the power of such AI models against each other until the problem of identifying (mis)-alignment is broken down into a manageable subtask. While the promise of this approach is clear, the original framework was based on the assumption that the honest strategy is able to simulate deterministic AI systems for an exponential number of steps, limiting its applicability. In this paper, we show how to address these challenges by designing a new set of debate protocols where the honest strategy can always succeed using a simulation of a polynomial number of steps, whilst being able to verify the alignment of stochastic AI systems, even when the dishonest strategy is allowed to use exponentially many simulation steps.

Reward models play a key role in aligning language model applications towards human preferences. However, this setup creates an incentive for the language model to exploit errors in the reward model to achieve high estimated reward, a phenomenon often termed reward hacking. A natural mitigation is to train an ensemble of reward models, aggregating over model outputs to obtain a more robust reward estimate. We explore the application of reward ensembles to alignment at both training time (through reinforcement learning) and inference time (through reranking). First, we show that reward models are underspecified: reward models that perform similarly in-distribution can yield very different rewards when used in alignment, due to distribution shift. Second, underspecification results in overoptimization, where alignment to one reward model does not improve reward as measured by another reward model trained on the same data. Third, overoptimization is mitigated by the use of reward ensembles, and ensembles that vary by their pretraining seeds lead to better generalization than ensembles that differ only by their fine-tuning seeds, with both outperforming individual reward models. However, even pretrain reward ensembles do not eliminate reward hacking: we show several qualitative reward hacking phenomena that are not mitigated by ensembling because all reward models in the ensemble exhibit similar error patterns.

Direct Preference Optimization (DPO) often struggles with long-chain mathematical reasoning. Existing approaches, such as Step-DPO, typically improve this by focusing on the first erroneous step in the reasoning chain. However, they overlook all other steps and rely heavily on humans or GPT-4 to identify erroneous steps. To address these issues, we propose Full-Step-DPO, a novel DPO framework tailored for mathematical reasoning. Instead of optimizing only the first erroneous step, it leverages step-wise rewards from the entire reasoning chain. This is achieved by training a self-supervised process reward model, which automatically scores each step, providing rewards while avoiding reliance on external signals. Furthermore, we introduce a novel step-wise DPO loss, which dynamically updates gradients based on these step-wise rewards. This endows stronger reasoning capabilities to language models. Extensive evaluations on both in-domain and out-of-domain mathematical reasoning benchmarks across various base language models, demonstrate that Full-Step-DPO achieves superior performance compared to state-of-the-art baselines.

From a first-principles perspective, it may seem odd that the strongest results in foundation model fine-tuning (FT) are achieved via a relatively complex, two-stage training procedure. Specifically, one first trains a reward model (RM) on some dataset (e.g. human preferences) before using it to provide online feedback as part of a downstream reinforcement learning (RL) procedure, rather than directly optimizing the policy parameters on the dataset via offline maximum likelihood estimation. In fact, from an information-theoretic perspective, we can only lose information via passing through a reward model and cannot create any new information via on-policy sampling. To explain this discrepancy, we scrutinize several hypotheses on the value of RL in FT through both theoretical and empirical lenses. Of the hypotheses considered, we find the most support for the explanation that on problems with a generation-verification gap, the combination of the ease of learning the relatively simple RM (verifier) from the preference data, coupled with the ability of the downstream RL procedure to then filter its search space to the subset of policies (generators) that are optimal for relatively simple verifiers is what leads to the superior performance of online FT.

Dueling bandits is a prominent framework for decision-making involving preferential feedback, a valuable feature that fits various applications involving human interaction, such as ranking, information retrieval, and recommendation systems. While substantial efforts have been made to minimize the cumulative regret in dueling bandits, a notable gap in the current research is the absence of regret bounds that account for the inherent uncertainty in pairwise comparisons between the dueling arms. Intuitively, greater uncertainty suggests a higher level of difficulty in the problem. To bridge this gap, this paper studies the problem of contextual dueling bandits, where the binary comparison of dueling arms is generated from a generalized linear model (GLM). We propose a new SupLinUCB-type algorithm that enjoys computational efficiency and a variance-aware regret bound tilde Obig(dsum_{t=1^Tsigma_t^2} + dbig), where sigma_t is the variance of the pairwise comparison in round t, d is the dimension of the context vectors, and T is the time horizon. Our regret bound naturally aligns with the intuitive expectation in scenarios where the comparison is deterministic, the algorithm only suffers from an tilde O(d) regret. We perform empirical experiments on synthetic data to confirm the advantage of our method over previous variance-agnostic algorithms.

We propose CURE, a novel reinforcement learning framework with a dedicated reward design that co-evolves coding and unit test generation capabilities based on their interaction outcomes, without any ground-truth code as supervision. This approach enables flexible and scalable training and allows the unit tester to learn directly from the coder's mistakes. Our derived ReasonFlux-Coder-7B and 14B models improve code generation accuracy by 5.3% and Best-of-N accuracy by 9.0% after optimization on Qwen2.5-Instruct models, outperforming similarly sized Qwen-Coder, DeepSeek-Coder, and Seed-Coder. They naturally extend to downstream tasks such as test-time scaling and agentic coding-achieving a 8.1% improvement over the base model. For the long-CoT model, our ReasonFlux-Coder-4B consistently outperforms Qwen3-4B while achieving 64.8% inference efficiency in unit test generation. Notably, we also find that our model can serve as an effective reward model for reinforcement learning on base models. Project: https://github.com/Gen-Verse/CURE

Reward models play a critical role in guiding large language models toward outputs that align with human expectations. However, an open challenge remains in effectively utilizing test-time compute to enhance reward model performance. In this work, we introduce Reward Reasoning Models (RRMs), which are specifically designed to execute a deliberate reasoning process before generating final rewards. Through chain-of-thought reasoning, RRMs leverage additional test-time compute for complex queries where appropriate rewards are not immediately apparent. To develop RRMs, we implement a reinforcement learning framework that fosters self-evolved reward reasoning capabilities without requiring explicit reasoning traces as training data. Experimental results demonstrate that RRMs achieve superior performance on reward modeling benchmarks across diverse domains. Notably, we show that RRMs can adaptively exploit test-time compute to further improve reward accuracy. The pretrained reward reasoning models are available at https://huggingface.co/Reward-Reasoning.

Reinforcement Learning from Human Feedback (RLHF) has become a crucial technology for aligning language models with human values and intentions, enabling models to produce more helpful and harmless responses. Reward models are trained as proxies for human preferences to drive reinforcement learning optimization. While reward models are often considered central to achieving high performance, they face the following challenges in practical applications: (1) Incorrect and ambiguous preference pairs in the dataset may hinder the reward model from accurately capturing human intent. (2) Reward models trained on data from a specific distribution often struggle to generalize to examples outside that distribution and are not suitable for iterative RLHF training. In this report, we attempt to address these two issues. (1) From a data perspective, we propose a method to measure the strength of preferences within the data, based on a voting mechanism of multiple reward models. Experimental results confirm that data with varying preference strengths have different impacts on reward model performance. We introduce a series of novel methods to mitigate the influence of incorrect and ambiguous preferences in the dataset and fully leverage high-quality preference data. (2) From an algorithmic standpoint, we introduce contrastive learning to enhance the ability of reward models to distinguish between chosen and rejected responses, thereby improving model generalization. Furthermore, we employ meta-learning to enable the reward model to maintain the ability to differentiate subtle differences in out-of-distribution samples, and this approach can be utilized for iterative RLHF optimization.

We introduce a new benchmark for reward models that quantifies their ability to produce strong language models through RLHF (Reinforcement Learning from Human Feedback). The gold-standard approach is to run a full RLHF training pipeline and directly probe downstream LLM performance. However, this process is prohibitively expensive. To address this, we build a predictive model of downstream LLM performance by evaluating the reward model on proxy tasks. These proxy tasks consist of a large-scale human preference and a verifiable correctness preference dataset, in which we measure 12 metrics across 12 domains. To investigate which reward model metrics are most correlated to gold-standard RLHF outcomes, we launch an end-to-end RLHF experiment on a large-scale crowdsourced human preference platform to view real reward model downstream performance as ground truth. Ultimately, we compile our data and findings into Preference Proxy Evaluations (PPE), the first reward model benchmark explicitly linked to post-RLHF real-world human preference performance, which we open-source for public use and further development. Our code and evaluations can be found at https://github.com/lmarena/PPE .

Large Language Models (LLMs) have demonstrated remarkable capabilities across various domains. Math Word Problems (MWPs) serve as a crucial benchmark for evaluating LLMs' reasoning abilities. While most research primarily focuses on improving accuracy, it often neglects understanding and addressing the underlying patterns of errors. Current error classification methods rely on static and predefined categories, which limit their ability to capture the full spectrum of error patterns in mathematical reasoning. To enable systematic error analysis, we collect error samples from 15 different LLMs of varying sizes across four distinct MWP datasets using multiple sampling strategies. Based on this extensive collection, we introduce MWPES-300K, a comprehensive dataset containing 304,865 error samples that cover diverse error patterns and reasoning paths. To reduce human bias and enable fine-grained analysis of error patterns, we propose a novel framework for automated dynamic error classification in mathematical reasoning. Experimental results demonstrate that dataset characteristics significantly shape error patterns, which evolve from basic to complex manifestations as model capabilities increase. With deeper insights into error patterns, we propose error-aware prompting that incorporates common error patterns as explicit guidance, leading to significant improvements in mathematical reasoning performance.

We introduce SafeWork-R1, a cutting-edge multimodal reasoning model that demonstrates the coevolution of capabilities and safety. It is developed by our proposed SafeLadder framework, which incorporates large-scale, progressive, safety-oriented reinforcement learning post-training, supported by a suite of multi-principled verifiers. Unlike previous alignment methods such as RLHF that simply learn human preferences, SafeLadder enables SafeWork-R1 to develop intrinsic safety reasoning and self-reflection abilities, giving rise to safety `aha' moments. Notably, SafeWork-R1 achieves an average improvement of 46.54% over its base model Qwen2.5-VL-72B on safety-related benchmarks without compromising general capabilities, and delivers state-of-the-art safety performance compared to leading proprietary models such as GPT-4.1 and Claude Opus 4. To further bolster its reliability, we implement two distinct inference-time intervention methods and a deliberative search mechanism, enforcing step-level verification. Finally, we further develop SafeWork-R1-InternVL3-78B, SafeWork-R1-DeepSeek-70B, and SafeWork-R1-Qwen2.5VL-7B. All resulting models demonstrate that safety and capability can co-evolve synergistically, highlighting the generalizability of our framework in building robust, reliable, and trustworthy general-purpose AI.

Reinforcement Learning algorithms that learn from human feedback (RLHF) need to be efficient in terms of statistical complexity, computational complexity, and query complexity. In this work, we consider the RLHF setting where the feedback is given in the format of preferences over pairs of trajectories. In the linear MDP model, using randomization in algorithm design, we present an algorithm that is sample efficient (i.e., has near-optimal worst-case regret bounds) and has polynomial running time (i.e., computational complexity is polynomial with respect to relevant parameters). Our algorithm further minimizes the query complexity through a novel randomized active learning procedure. In particular, our algorithm demonstrates a near-optimal tradeoff between the regret bound and the query complexity. To extend the results to more general nonlinear function approximation, we design a model-based randomized algorithm inspired by the idea of Thompson sampling. Our algorithm minimizes Bayesian regret bound and query complexity, again achieving a near-optimal tradeoff between these two quantities. Computation-wise, similar to the prior Thompson sampling algorithms under the regular RL setting, the main computation primitives of our algorithm are Bayesian supervised learning oracles which have been heavily investigated on the empirical side when applying Thompson sampling algorithms to RL benchmark problems.

Reinforcement Learning from Human Feedback (RLHF) is crucial for aligning large language models with human preferences. While recent research has focused on algorithmic improvements, the importance of prompt-data construction has been overlooked. This paper addresses this gap by exploring data-driven bottlenecks in RLHF performance scaling, particularly reward hacking and decreasing response diversity. We introduce a hybrid reward system combining reasoning task verifiers (RTV) and a generative reward model (GenRM) to mitigate reward hacking. We also propose a novel prompt-selection method, Pre-PPO, to maintain response diversity and enhance learning effectiveness. Additionally, we find that prioritizing mathematical and coding tasks early in RLHF training significantly improves performance. Experiments across two model sizes validate our methods' effectiveness and scalability. Results show that RTV is most resistant to reward hacking, followed by GenRM with ground truth, and then GenRM with SFT Best-of-N responses. Our strategies enable rapid capture of subtle task-specific distinctions, leading to substantial improvements in overall RLHF performance. This work highlights the importance of careful data construction and provides practical methods to overcome performance barriers in RLHF.

Offline reinforcement learning enables agents to leverage large pre-collected datasets of environment transitions to learn control policies, circumventing the need for potentially expensive or unsafe online data collection. Significant progress has been made recently in offline model-based reinforcement learning, approaches which leverage a learned dynamics model. This typically involves constructing a probabilistic model, and using the model uncertainty to penalize rewards where there is insufficient data, solving for a pessimistic MDP that lower bounds the true MDP. Existing methods, however, exhibit a breakdown between theory and practice, whereby pessimistic return ought to be bounded by the total variation distance of the model from the true dynamics, but is instead implemented through a penalty based on estimated model uncertainty. This has spawned a variety of uncertainty heuristics, with little to no comparison between differing approaches. In this paper, we compare these heuristics, and design novel protocols to investigate their interaction with other hyperparameters, such as the number of models, or imaginary rollout horizon. Using these insights, we show that selecting these key hyperparameters using Bayesian Optimization produces superior configurations that are vastly different to those currently used in existing hand-tuned state-of-the-art methods, and result in drastically stronger performance.

Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter beta is considerably large in the theorem and chosen heuristically in practice. Then, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which follows the Gamma distribution, to mitigate the impact of manually specifying beta. This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. Furthermore, we propose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential distribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not require an increase in the confidence parameter in terms of the number of iterations, which avoids over-exploration in the later iterations. Finally, we demonstrate the effectiveness of IRGP-UCB through extensive experiments.

Budget management strategies in repeated auctions have received growing attention in online advertising markets. However, previous work on budget management in online bidding mainly focused on second-price auctions. The rapid shift from second-price auctions to first-price auctions for online ads in recent years has motivated the challenging question of how to bid in repeated first-price auctions while controlling budgets. In this work, we study the problem of learning in repeated first-price auctions with budgets. We design a dual-based algorithm that can achieve a near-optimal O(T) regret with full information feedback where the maximum competing bid is always revealed after each auction. We further consider the setting with one-sided information feedback where only the winning bid is revealed after each auction. We show that our modified algorithm can still achieve an O(T) regret with mild assumptions on the bidder's value distribution. Finally, we complement the theoretical results with numerical experiments to confirm the effectiveness of our budget management policy.

Best-of-N decoding methods instruct large language models (LLMs) to generate multiple solutions, score each using a scoring function, and select the highest scored as the final answer to mathematical reasoning problems. However, this repeated independent process often leads to the same mistakes, making the selected solution still incorrect. We propose a novel prompting method named Stepwise Correction (StepCo) that helps LLMs identify and revise incorrect steps in their generated reasoning paths. It iterates verification and revision phases that employ a process-supervised verifier. The verify-then-revise process not only improves answer correctness but also reduces token consumption with fewer paths needed to generate. With StepCo, a series of LLMs demonstrate exceptional performance. Notably, using GPT-4o as the backend LLM, StepCo achieves an average accuracy of 94.1 across eight datasets, significantly outperforming the state-of-the-art Best-of-N method by +2.4, while reducing token consumption by 77.8%.

Selecting the best code solution from multiple generated ones is an essential task in code generation, which can be achieved by using some reliable validators (e.g., developer-written test cases) for assistance. Since reliable test cases are not always available and can be expensive to build in practice, researchers propose to automatically generate test cases to assess code solutions. However, when both code solutions and test cases are plausible and not reliable, selecting the best solution becomes challenging. Although some heuristic strategies have been proposed to tackle this problem, they lack a strong theoretical guarantee and it is still an open question whether an optimal selection strategy exists. Our work contributes in two ways. First, we show that within a Bayesian framework, the optimal selection strategy can be defined based on the posterior probability of the observed passing states between solutions and tests. The problem of identifying the best solution is then framed as an integer programming problem. Second, we propose an efficient approach for approximating this optimal (yet uncomputable) strategy, where the approximation error is bounded by the correctness of prior knowledge. We then incorporate effective prior knowledge to tailor code generation tasks. Both theoretical and empirical studies confirm that existing heuristics are limited in selecting the best solutions with plausible test cases. Our proposed approximated optimal strategy B4 significantly surpasses existing heuristics in selecting code solutions generated by large language models (LLMs) with LLM-generated tests, achieving a relative performance improvement by up to 50% over the strongest heuristic and 246% over the random selection in the most challenging scenarios. Our code is publicly available at https://github.com/ZJU-CTAG/B4.

Reward design is a fundamental, yet challenging aspect of practical reinforcement learning (RL). For simple tasks, researchers typically handcraft the reward function, e.g., using a linear combination of several reward factors. However, such reward engineering is subject to approximation bias, incurs large tuning cost, and often cannot provide the granularity required for complex tasks. To avoid these difficulties, researchers have turned to reinforcement learning from human feedback (RLHF), which learns a reward function from human preferences between pairs of trajectory sequences. By leveraging preference-based reward modeling, RLHF learns complex rewards that are well aligned with human preferences, allowing RL to tackle increasingly difficult problems. Unfortunately, the applicability of RLHF is limited due to the high cost and difficulty of obtaining human preference data. In light of this cost, we investigate learning reward functions for complex tasks with less human effort; simply by ranking the importance of the reward factors. More specifically, we propose a new RL framework -- HERON, which compares trajectories using a hierarchical decision tree induced by the given ranking. These comparisons are used to train a preference-based reward model, which is then used for policy learning. We find that our framework can not only train high performing agents on a variety of difficult tasks, but also provide additional benefits such as improved sample efficiency and robustness. Our code is available at https://github.com/abukharin3/HERON.

Complex multi-step reasoning tasks, such as solving mathematical problems or generating code, remain a significant hurdle for even the most advanced large language models (LLMs). Verifying LLM outputs with an Outcome Reward Model (ORM) is a standard inference-time technique aimed at enhancing the reasoning performance of LLMs. However, this still proves insufficient for reasoning tasks with a lengthy or multi-hop reasoning chain, where the intermediate outcomes are neither properly rewarded nor penalized. Process supervision addresses this limitation by assigning intermediate rewards during the reasoning process. To date, the methods used to collect process supervision data have relied on either human annotation or per-step Monte Carlo estimation, both prohibitively expensive to scale, thus hindering the broad application of this technique. In response to this challenge, we propose a novel divide-and-conquer style Monte Carlo Tree Search (MCTS) algorithm named OmegaPRM for the efficient collection of high-quality process supervision data. This algorithm swiftly identifies the first error in the Chain of Thought (CoT) with binary search and balances the positive and negative examples, thereby ensuring both efficiency and quality. As a result, we are able to collect over 1.5 million process supervision annotations to train a Process Reward Model (PRM). Utilizing this fully automated process supervision alongside the weighted self-consistency algorithm, we have enhanced the instruction tuned Gemini Pro model's math reasoning performance, achieving a 69.4\% success rate on the MATH benchmark, a 36\% relative improvement from the 51\% base model performance. Additionally, the entire process operates without any human intervention, making our method both financially and computationally cost-effective compared to existing methods.

In recommender system or crowdsourcing applications of online learning, a human's preferences or abilities are often a function of the algorithm's recent actions. Motivated by this, a significant line of work has formalized settings where an action's loss is a function of the number of times that action was recently played in the prior m timesteps, where m corresponds to a bound on human memory capacity. To more faithfully capture decay of human memory with time, we introduce the Weighted Tallying Bandit (WTB), which generalizes this setting by requiring that an action's loss is a function of a weighted summation of the number of times that arm was played in the last m timesteps. This WTB setting is intractable without further assumption. So we study it under Repeated Exposure Optimality (REO), a condition motivated by the literature on human physiology, which requires the existence of an action that when repetitively played will eventually yield smaller loss than any other sequence of actions. We study the minimization of the complete policy regret (CPR), which is the strongest notion of regret, in WTB under REO. Since m is typically unknown, we assume we only have access to an upper bound M on m. We show that for problems with K actions and horizon T, a simple modification of the successive elimination algorithm has O left( KT + (m+M)K right) CPR. Interestingly, upto an additive (in lieu of mutliplicative) factor in (m+M)K, this recovers the classical guarantee for the simpler stochastic multi-armed bandit with traditional regret. We additionally show that in our setting, any algorithm will suffer additive CPR of Omega left( mK + M right), demonstrating our result is nearly optimal. Our algorithm is computationally efficient, and we experimentally demonstrate its practicality and superiority over natural baselines.

Large Language Models (LLMs) have shown tremendous potential as agents, excelling at tasks that require multiple rounds of reasoning and interactions. Rejection Sampling Fine-Tuning (RFT) has emerged as an effective method for finetuning LLMs as agents: it first imitates expert-generated successful trajectories and further improves agentic skills through iterative fine-tuning on successful, self-generated trajectories. However, since the expert (e.g., GPT-4) succeeds primarily on simpler subtasks and RFT inherently favors simpler scenarios, many complex subtasks remain unsolved and persistently out-of-distribution (OOD). Upon investigating these challenging subtasks, we discovered that previously failed expert trajectories can often provide valuable guidance, e.g., plans and key actions, that can significantly improve agent exploration efficiency and acquisition of critical skills. Motivated by these observations, we propose Exploring Expert Failures (EEF), which identifies beneficial actions from failed expert trajectories and integrates them into the training dataset. Potentially harmful actions are meticulously excluded to prevent contamination of the model learning process. By leveraging the beneficial actions in expert failures, EEF successfully solves some previously unsolvable subtasks and improves agent tuning performance. Remarkably, our approach achieved a 62\% win rate in WebShop, outperforming RFT (53. 6\%) and GPT-4 (35. 6\%), and to the best of our knowledge, setting a new state-of-the-art as the first method to surpass a score of 0.81 in WebShop and exceed 81 in SciWorld.

Motivated by concerns about making online decisions that incur undue amount of risk at each time step, in this paper, we formulate the probably anytime-safe stochastic combinatorial semi-bandits problem. In this problem, the agent is given the option to select a subset of size at most K from a set of L ground items. Each item is associated to a certain mean reward as well as a variance that represents its risk. To mitigate the risk that the agent incurs, we require that with probability at least 1-delta, over the entire horizon of time T, each of the choices that the agent makes should contain items whose sum of variances does not exceed a certain variance budget. We call this probably anytime-safe constraint. Under this constraint, we design and analyze an algorithm {\sc PASCombUCB} that minimizes the regret over the horizon of time T. By developing accompanying information-theoretic lower bounds, we show that under both the problem-dependent and problem-independent paradigms, {\sc PASCombUCB} is almost asymptotically optimal. Experiments are conducted to corroborate our theoretical findings. Our problem setup, the proposed {\sc PASCombUCB} algorithm, and novel analyses are applicable to domains such as recommendation systems and transportation in which an agent is allowed to choose multiple items at a single time step and wishes to control the risk over the whole time horizon.

We consider an online learning problem with one-sided feedback, in which the learner is able to observe the true label only for positively predicted instances. On each round, k instances arrive and receive classification outcomes according to a randomized policy deployed by the learner, whose goal is to maximize accuracy while deploying individually fair policies. We first extend the framework of Bechavod et al. (2020), which relies on the existence of a human fairness auditor for detecting fairness violations, to instead incorporate feedback from dynamically-selected panels of multiple, possibly inconsistent, auditors. We then construct an efficient reduction from our problem of online learning with one-sided feedback and a panel reporting fairness violations to the contextual combinatorial semi-bandit problem (Cesa-Bianchi & Lugosi, 2009, Gy\"{o}rgy et al., 2007). Finally, we show how to leverage the guarantees of two algorithms in the contextual combinatorial semi-bandit setting: Exp2 (Bubeck et al., 2012) and the oracle-efficient Context-Semi-Bandit-FTPL (Syrgkanis et al., 2016), to provide multi-criteria no regret guarantees simultaneously for accuracy and fairness. Our results eliminate two potential sources of bias from prior work: the "hidden outcomes" that are not available to an algorithm operating in the full information setting, and human biases that might be present in any single human auditor, but can be mitigated by selecting a well chosen panel.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a powerful paradigm for facilitating the self-improvement of large language models (LLMs), particularly in the domain of complex reasoning tasks. However, prevailing on-policy RL methods often contend with significant training instability and inefficiency. This is primarily due to a capacity-difficulty mismatch, where the complexity of training data frequently outpaces the model's current capabilities, leading to critically sparse reward signals and stalled learning progress. This challenge is particularly acute for smaller, more resource-efficient LLMs. To overcome this, we introduce the Guided Hybrid Policy Optimization (GHPO), a novel difficulty-aware reinforcement learning framework. GHPO dynamically calibrates task difficulty by employing adaptive prompt refinement to provide targeted guidance. This unique approach adaptively balances direct imitation learning for problems currently beyond the model's reach with exploration-based reinforcement learning for more manageable tasks, effectively creating a smooth and optimized learning curriculum. Extensive experiments demonstrate that GHPO achieves an average performance gain of approximately 5% across six challenging mathematics benchmarks, consistently outperforming strong on-policy reinforcement learning and curriculum learning baselines. Further analysis confirms that our framework significantly enhances both training stability and final reasoning performance, thus offering a scalable and efficient solution for developing powerful and robust reasoning models.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

Many problems, such as online ad display, can be formulated as online bipartite matching. The crucial challenge lies in the nature of sequentially-revealed online item information, based on which we make irreversible matching decisions at each step. While numerous expert online algorithms have been proposed with bounded worst-case competitive ratios, they may not offer satisfactory performance in average cases. On the other hand, reinforcement learning (RL) has been applied to improve the average performance, but it lacks robustness and can perform arbitrarily poorly. In this paper, we propose a novel RL-based approach to edge-weighted online bipartite matching with robustness guarantees (LOMAR), achieving both good average-case and worst-case performance. The key novelty of LOMAR is a new online switching operation which, based on a judicious condition to hedge against future uncertainties, decides whether to follow the expert's decision or the RL decision for each online item. We prove that for any rhoin[0,1], LOMAR is rho-competitive against any given expert online algorithm. To improve the average performance, we train the RL policy by explicitly considering the online switching operation. Finally, we run empirical experiments to demonstrate the advantages of LOMAR compared to existing baselines. Our code is available at: https://github.com/Ren-Research/LOMAR

We investigate reinforcement learning (RL) for privileged planning in autonomous driving. State-of-the-art approaches for this task are rule-based, but these methods do not scale to the long tail. RL, on the other hand, is scalable and does not suffer from compounding errors like imitation learning. Contemporary RL approaches for driving use complex shaped rewards that sum multiple individual rewards, \eg~progress, position, or orientation rewards. We show that PPO fails to optimize a popular version of these rewards when the mini-batch size is increased, which limits the scalability of these approaches. Instead, we propose a new reward design based primarily on optimizing a single intuitive reward term: route completion. Infractions are penalized by terminating the episode or multiplicatively reducing route completion. We find that PPO scales well with higher mini-batch sizes when trained with our simple reward, even improving performance. Training with large mini-batch sizes enables efficient scaling via distributed data parallelism. We scale PPO to 300M samples in CARLA and 500M samples in nuPlan with a single 8-GPU node. The resulting model achieves 64 DS on the CARLA longest6 v2 benchmark, outperforming other RL methods with more complex rewards by a large margin. Requiring only minimal adaptations from its use in CARLA, the same method is the best learning-based approach on nuPlan. It scores 91.3 in non-reactive and 90.6 in reactive traffic on the Val14 benchmark while being an order of magnitude faster than prior work.

While recent advances have boosted LM proficiency in linguistic benchmarks, LMs consistently struggle to reason correctly on complex tasks like mathematics. We turn to Reinforcement Learning from Human Feedback (RLHF) as a method with which to shape model reasoning processes. In particular, we explore two reward schemes, outcome-supervised reward models (ORMs) and process-supervised reward models (PRMs), to optimize for logical reasoning. Our results show that the fine-grained reward provided by PRM-based methods enhances accuracy on simple mathematical reasoning (GSM8K) while, unexpectedly, reducing performance in complex tasks (MATH). Furthermore, we show the critical role reward aggregation functions play in model performance. Providing promising avenues for future research, our study underscores the need for further exploration into fine-grained reward modeling for more reliable language models.

Training models to effectively use test-time compute is crucial for improving the reasoning performance of LLMs. Current methods mostly do so via fine-tuning on search traces or running RL with 0/1 outcome reward, but do these approaches efficiently utilize test-time compute? Would these approaches continue to scale as the budget improves? In this paper, we try to answer these questions. We formalize the problem of optimizing test-time compute as a meta-reinforcement learning (RL) problem, which provides a principled perspective on spending test-time compute. This perspective enables us to view the long output stream from the LLM as consisting of several episodes run at test time and leads us to use a notion of cumulative regret over output tokens as a way to measure the efficacy of test-time compute. Akin to how RL algorithms can best tradeoff exploration and exploitation over training, minimizing cumulative regret would also provide the best balance between exploration and exploitation in the token stream. While we show that state-of-the-art models do not minimize regret, one can do so by maximizing a dense reward bonus in conjunction with the outcome 0/1 reward RL. This bonus is the ''progress'' made by each subsequent block in the output stream, quantified by the change in the likelihood of eventual success. Using these insights, we develop Meta Reinforcement Fine-Tuning, or MRT, a new class of fine-tuning methods for optimizing test-time compute. MRT leads to a 2-3x relative gain in performance and roughly a 1.5x gain in token efficiency for math reasoning compared to outcome-reward RL.

Reinforcement learning (RL) has been widely used in training large language models~(LLMs) for preventing unexpected outputs, \eg reducing harmfulness and errors. However, existing RL methods mostly adopt the instance-level reward, which is unable to provide fine-grained supervision for complex reasoning tasks, and can not focus on the few key tokens that lead to the incorrectness. To address it, we propose a new RL method named RLMEC that incorporates a generative model as the reward model, which is trained by the erroneous solution rewriting task under the minimum editing constraint, and can produce token-level rewards for RL training. Based on the generative reward model, we design the token-level RL objective for training and an imitation-based regularization for stabilizing RL process. And the both objectives focus on the learning of the key tokens for the erroneous solution, reducing the effect of other unimportant tokens. The experiment results on mathematical tasks and question-answering tasks have demonstrated the effectiveness of our approach. Our code and data are available at https://github.com/RUCAIBox/RLMEC.

Legal judgment prediction (LJP) aims to function as a judge by making final rulings based on case claims and facts, which plays a vital role in the judicial domain for supporting court decision-making and improving judicial efficiency. However, existing methods often struggle with logical errors when conducting complex legal reasoning. We propose LegalReasoner, which enhances LJP reliability through step-wise verification and correction of the reasoning process. Specifically, it first identifies dispute points to decompose complex cases, and then conducts step-wise reasoning while employing a process verifier to validate each step's logic from correctness, progressiveness, and potential perspectives. When errors are detected, expert-designed attribution and resolution strategies are applied for correction. To fine-tune LegalReasoner, we release the LegalHK dataset, containing 58,130 Hong Kong court cases with detailed annotations of dispute points, step-by-step reasoning chains, and process verification labels. Experiments demonstrate that LegalReasoner significantly improves concordance with court decisions from 72.37 to 80.27 on LLAMA-3.1-70B. The data is available at https://huggingface.co/datasets/weijiezz/LegalHK.

In recent years, Large Language Models (LLMs) have demonstrated remarkable generative abilities, but can they judge the quality of their own generations? A popular concept, referred to as self-refinement, postulates that LLMs can detect and correct the errors in their generations when asked to do so. However, recent empirical evidence points in the opposite direction, suggesting that LLMs often struggle to accurately identify errors when reasoning is involved. To address this, we propose a reasoning with refinement objective called ART: Ask, Refine, and Trust, which asks necessary questions to decide when an LLM should refine its output, and either affirm or withhold trust in its refinement by ranking the refinement and the initial prediction. On two multistep reasoning tasks of mathematical word problems (GSM8K) and question answering (StrategyQA), ART achieves a performance gain of +5 points over self-refinement baselines, while using a much smaller model as the decision maker. We also demonstrate the benefit of using smaller models to make refinement decisions as a cost-effective alternative to fine-tuning a larger model.

Reward models are critical in techniques like Reinforcement Learning from Human Feedback (RLHF) and Inference Scaling Laws, where they guide language model alignment and select optimal responses. Despite their importance, existing reward model benchmarks often evaluate models by asking them to distinguish between responses generated by models of varying power. However, this approach fails to assess reward models on subtle but critical content changes and variations in style, resulting in a low correlation with policy model performance. To this end, we introduce RM-Bench, a novel benchmark designed to evaluate reward models based on their sensitivity to subtle content differences and resistance to style biases. Extensive experiments demonstrate that RM-Bench strongly correlates with policy model performance, making it a reliable reference for selecting reward models to align language models effectively. We evaluate nearly 40 reward models on RM-Bench. Our results reveal that even state-of-the-art models achieve an average performance of only 46.6%, which falls short of random-level accuracy (50%) when faced with style bias interference. These findings highlight the significant room for improvement in current reward models. Related code and data are available at https://github.com/THU-KEG/RM-Bench.

Recent studies on post-training large language models (LLMs) for reasoning through reinforcement learning (RL) typically focus on tasks that can be accurately verified and rewarded, such as solving math problems. In contrast, our research investigates the impact of reward noise, a more practical consideration for real-world scenarios involving the post-training of LLMs using reward models. We found that LLMs demonstrate strong robustness to substantial reward noise. For example, manually flipping 40% of the reward function's outputs in math tasks still allows a Qwen-2.5-7B model to achieve rapid convergence, improving its performance on math tasks from 5% to 72%, compared to the 75% accuracy achieved by a model trained with noiseless rewards. Surprisingly, by only rewarding the appearance of key reasoning phrases (namely reasoning pattern reward, RPR), such as ``first, I need to''-without verifying the correctness of answers, the model achieved peak downstream performance (over 70% accuracy for Qwen-2.5-7B) comparable to models trained with strict correctness verification and accurate rewards. Recognizing the importance of the reasoning process over the final results, we combined RPR with noisy reward models. RPR helped calibrate the noisy reward models, mitigating potential false negatives and enhancing the LLM's performance on open-ended tasks. These findings suggest the importance of improving models' foundational abilities during the pre-training phase while providing insights for advancing post-training techniques. Our code and scripts are available at https://github.com/trestad/Noisy-Rewards-in-Learning-to-Reason.

Large Reasoning Models (LRMs) exhibit remarkable reasoning abilities but rely primarily on parametric knowledge, limiting factual accuracy. While recent works equip reinforcement learning (RL)-based LRMs with retrieval capabilities, they suffer from overthinking and lack robustness in reasoning, reducing their effectiveness in question answering (QA) tasks. To address this, we propose ReaRAG, a factuality-enhanced reasoning model that explores diverse queries without excessive iterations. Our solution includes a novel data construction framework with an upper bound on the reasoning chain length. Specifically, we first leverage an LRM to generate deliberate thinking, then select an action from a predefined action space (Search and Finish). For Search action, a query is executed against the RAG engine, where the result is returned as observation to guide reasoning steps later. This process iterates until a Finish action is chosen. Benefiting from ReaRAG's strong reasoning capabilities, our approach outperforms existing baselines on multi-hop QA. Further analysis highlights its strong reflective ability to recognize errors and refine its reasoning trajectory. Our study enhances LRMs' factuality while effectively integrating robust reasoning for Retrieval-Augmented Generation (RAG).

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness requirements. These requirements can be imposed (with generalization guarantees) by formulating constrained learning problems that can then be tackled by dual ascent algorithms. Yet, though these algorithms converge in objective value, even in non-convex settings, they cannot guarantee that their outcome is feasible. Doing so requires randomizing over all iterates, which is impractical in virtually any modern applications. Still, final iterates have been observed to perform well in practice. In this work, we address this gap between theory and practice by characterizing the constraint violation of Lagrangian minimizers associated with optimal dual variables, despite lack of convexity. To do this, we leverage the fact that non-convex, finite-dimensional constrained learning problems can be seen as parametrizations of convex, functional problems. Our results show that rich parametrizations effectively mitigate the issue of feasibility in dual methods, shedding light on prior empirical successes of dual learning. We illustrate our findings in fair learning tasks.

Reinforcement Learning from Human Feedback (RLHF) is a pivotal technique that aligns language models closely with human-centric values. The initial phase of RLHF involves learning human values using a reward model from ranking data. It is observed that the performance of the reward model degrades after one epoch of training, and optimizing too much against the learned reward model eventually hinders the true objective. This paper delves into these issues, leveraging the theoretical insights to design improved reward learning algorithm termed 'Iterative Data Smoothing' (IDS). The core idea is that during each training epoch, we not only update the model with the data, but also update the date using the model, replacing hard labels with soft labels. Our empirical findings highlight the superior performance of this approach over the traditional methods.

Language models (LMs) can produce errors that are hard to detect for humans, especially when the task is complex. RLHF, the most popular post-training method, may exacerbate this problem: to achieve higher rewards, LMs might get better at convincing humans that they are right even when they are wrong. We study this phenomenon under a standard RLHF pipeline, calling it "U-SOPHISTRY" since it is Unintended by model developers. Specifically, we ask time-constrained (e.g., 3-10 minutes) human subjects to evaluate the correctness of model outputs and calculate humans' accuracy against gold labels. On a question-answering task (QuALITY) and programming task (APPS), RLHF makes LMs better at convincing our subjects but not at completing the task correctly. RLHF also makes the model harder to evaluate: our subjects' false positive rate increases by 24.1% on QuALITY and 18.3% on APPS. Finally, we show that probing, a state-of-the-art approach for detecting Intended Sophistry (e.g. backdoored LMs), does not generalize to U-SOPHISTRY. Our results highlight an important failure mode of RLHF and call for more research in assisting humans to align them.

Ensuring safety in Reinforcement Learning (RL), typically framed as a Constrained Markov Decision Process (CMDP), is crucial for real-world exploration applications. Current approaches in handling CMDP struggle to balance optimality and feasibility, as direct optimization methods cannot ensure state-wise in-training safety, and projection-based methods correct actions inefficiently through lengthy iterations. To address these challenges, we propose Adaptive Chance-constrained Safeguards (ACS), an adaptive, model-free safe RL algorithm using the safety recovery rate as a surrogate chance constraint to iteratively ensure safety during exploration and after achieving convergence. Theoretical analysis indicates that the relaxed probabilistic constraint sufficiently guarantees forward invariance to the safe set. And extensive experiments conducted on both simulated and real-world safety-critical tasks demonstrate its effectiveness in enforcing safety (nearly zero-violation) while preserving optimality (+23.8%), robustness, and fast response in stochastic real-world settings.

We consider an extension to the classic position auctions in which sponsored creatives can be added within AI generated content rather than shown in predefined slots. New challenges arise from the natural requirement that sponsored creatives should smoothly fit into the context. With the help of advanced LLM technologies, it becomes viable to accurately estimate the benefits of adding each individual sponsored creatives into each potential positions within the AI generated content by properly taking the context into account. Therefore, we assume one click-through rate estimation for each position-creative pair, rather than one uniform estimation for each sponsored creative across all positions in classic settings. As a result, the underlying optimization becomes a general matching problem, thus the substitution effects should be treated more carefully compared to standard position auction settings, where the slots are independent with each other. In this work, we formalize a concrete mathematical model of the extended position auction problem and study the welfare-maximization and revenue-maximization mechanism design problem. Formally, we consider two different user behavior models and solve the mechanism design problems therein respectively. For the Multinomial Logit (MNL) model, which is order-insensitive, we can efficiently implement the optimal mechanisms. For the cascade model, which is order-sensitive, we provide approximately optimal solutions.

Early time classification algorithms aim to label a stream of features without processing the full input stream, while maintaining accuracy comparable to that achieved by applying the classifier to the entire input. In this paper, we introduce a statistical framework that can be applied to any sequential classifier, formulating a calibrated stopping rule. This data-driven rule attains finite-sample, distribution-free control of the accuracy gap between full and early-time classification. We start by presenting a novel method that builds on the Learn-then-Test calibration framework to control this gap marginally, on average over i.i.d. instances. As this algorithm tends to yield an excessively high accuracy gap for early halt times, our main contribution is the proposal of a framework that controls a stronger notion of error, where the accuracy gap is controlled conditionally on the accumulated halt times. Numerical experiments demonstrate the effectiveness, applicability, and usefulness of our method. We show that our proposed early stopping mechanism reduces up to 94% of timesteps used for classification while achieving rigorous accuracy gap control.

Uncertainty in perception, actuation, and the environment often require multiple attempts for a robotic task to be successful. We study a class of problems providing (1) low-entropy indicators of terminal success / failure, and (2) unreliable (high-entropy) data to predict the final outcome of an ongoing task. Examples include a robot trying to connect with a charging station, parallel parking, or assembling a tightly-fitting part. The ability to restart after predicting failure early, versus simply running to failure, can significantly decrease the makespan, that is, the total time to completion, with the drawback of potentially short-cutting an otherwise successful operation. Assuming task running times to be Poisson distributed, and using a Markov Jump process to capture the dynamics of the underlying Markov Decision Process, we derive a closed form solution that predicts makespan based on the confusion matrix of the failure predictor. This allows the robot to learn failure prediction in a production environment, and only adopt a preemptive policy when it actually saves time. We demonstrate this approach using a robotic peg-in-hole assembly problem using a real robotic system. Failures are predicted by a dilated convolutional network based on force-torque data, showing an average makespan reduction from 101s to 81s (N=120, p<0.05). We posit that the proposed algorithm generalizes to any robotic behavior with an unambiguous terminal reward, with wide ranging applications on how robots can learn and improve their behaviors in the wild.

Supervised fine-tuning (SFT) is a milestone in aligning large language models with human instructions and adapting them to downstream tasks. In particular, Low-Rank Adaptation (LoRA) has gained widespread attention due to its parameter efficiency. However, its impact on improving the performance of large models remains limited. Recent studies suggest that combining LoRA with Mixture-of-Experts (MoE) can significantly enhance fine-tuning performance. MoE adapts to the diversity and complexity of datasets by dynamically selecting the most suitable experts, thereby improving task accuracy and efficiency. Despite impressive results, recent studies reveal issues in the MoE routing mechanism, such as incorrect assignments and imbalanced expert allocation. Inspired by the principles of Redundancy and Fault Tolerance Theory. We innovatively integrate the concept of Mixture of Experts into the routing mechanism and propose an efficient fine-tuning method called Mixture of Routers (MoR). It employs multiple sub-routers for joint selection and uses a learnable main router to determine the weights of the sub-routers. The results show that MoR outperforms baseline models on most tasks, achieving an average performance improvement of 1%. MoR can serve as a plug-and-play, parameter-efficient fine-tuning method suitable for a wide range of applications. Our code is available here: https://anonymous.4open.science/r/MoR-DFC6.

Equipping agents with the capacity to justify made decisions using supporting evidence represents a cornerstone of accountable decision-making. Furthermore, ensuring that justifications are in line with human expectations and societal norms is vital, especially in high-stakes situations such as healthcare. In this work, we propose the use of a debate-based reward model for reinforcement learning agents, where the outcome of a zero-sum debate game quantifies the justifiability of a decision in a particular state. This reward model is then used to train a justifiable policy, whose decisions can be more easily corroborated with supporting evidence. In the debate game, two argumentative agents take turns providing supporting evidence for two competing decisions. Given the proposed evidence, a proxy of a human judge evaluates which decision is better justified. We demonstrate the potential of our approach in learning policies for prescribing and justifying treatment decisions of septic patients. We show that augmenting the reward with the feedback signal generated by the debate-based reward model yields policies highly favored by the judge when compared to the policy obtained solely from the environment rewards, while hardly sacrificing any performance. Moreover, in terms of the overall performance and justifiability of trained policies, the debate-based feedback is comparable to the feedback obtained from an ideal judge proxy that evaluates decisions using the full information encoded in the state. This suggests that the debate game outputs key information contained in states that is most relevant for evaluating decisions, which in turn substantiates the practicality of combining our approach with human-in-the-loop evaluations. Lastly, we showcase that agents trained via multi-agent debate learn to propose evidence that is resilient to refutations and closely aligns with human preferences.

Aligning the behavior of Large language models (LLMs) with human intentions and values remains a critical challenge. Reinforcement learning from human feedback (RLHF) aligns LLMs by training a reward model (RM) on human preferences and fine-tuning the LLMs to maximize RM feedback. Despite its effectiveness and popularity, RLHF is prone to biased local optimization. It means RM fails to provide feedback that accurately aligns with human preference, causing LLMs to explore unexpected generalizations, and failing to achieve alignment objectives. To mitigate this issue, we propose a novel sequence-to-sequence (seq2seq) reward modeling method. Its key insight is that learning from language feedback rather than scalar feedback improves RLHF without additional annotations. We replaced the reward modeling target from binary maximum likelihood estimation (MLE) with sequence MLE. This method enables richer and fine-grained language feedback without additional annotations, models, or training stages. Our experiments demonstrated its effectiveness, specifically, reducing the refusal-to-response paradigm in single-turn safety dialogues and the long-response bias in text summarization tasks. We provide further analysis that seq2seq RM improves RLHF performance across 2B and 7B LLMs on 3 NLP tasks, achieving an average win rate of 76.9\%. We further show that seq2seq RM can still improve the performance of RLHF under out-of-distribution prompts.

Large Reasoning Models (LRMs) have shown remarkable capabilities in solving complex problems through reinforcement learning (RL), particularly by generating long reasoning traces. However, these extended outputs often exhibit substantial redundancy, which limits the efficiency of LRMs. In this paper, we investigate RL-based approaches to promote reasoning efficiency. Specifically, we first present a unified framework that formulates various efficient reasoning methods through the lens of length-based reward shaping. Building on this perspective, we propose a novel Length-bAsed StEp Reward shaping method (LASER), which employs a step function as the reward, controlled by a target length. LASER surpasses previous methods, achieving a superior Pareto-optimal balance between performance and efficiency. Next, we further extend LASER based on two key intuitions: (1) The reasoning behavior of the model evolves during training, necessitating reward specifications that are also adaptive and dynamic; (2) Rather than uniformly encouraging shorter or longer chains of thought (CoT), we posit that length-based reward shaping should be difficulty-aware i.e., it should penalize lengthy CoTs more for easy queries. This approach is expected to facilitate a combination of fast and slow thinking, leading to a better overall tradeoff. The resulting method is termed LASER-D (Dynamic and Difficulty-aware). Experiments on DeepSeek-R1-Distill-Qwen-1.5B, DeepSeek-R1-Distill-Qwen-7B, and DeepSeek-R1-Distill-Qwen-32B show that our approach significantly enhances both reasoning performance and response length efficiency. For instance, LASER-D and its variant achieve a +6.1 improvement on AIME2024 while reducing token usage by 63%. Further analysis reveals our RL-based compression produces more concise reasoning patterns with less redundant "self-reflections". Resources are at https://github.com/hkust-nlp/Laser.

Reward modeling in large language models is susceptible to reward hacking, causing models to latch onto superficial features such as the tendency to generate lists or unnecessarily long responses. In reinforcement learning from human feedback (RLHF) and more generally during post-training flawed reward signals often lead to outputs that optimize for these spurious correlates instead of genuine quality or correctness. We propose Context-Aware Reward Modeling (CARMO), a novel approach that first generates dynamic, context-relevant criteria to ground the reward model before producing reward scores. Unlike prior methods that rely on static rubrics, CARMO leverages large language models (LLMs) to adaptively create evaluation criteria such as logical consistency, clarity, and depth tailored to the user query. Our theoretical analysis shows that such criteria generation can mitigate reward hacking. We further demonstrate that CARMO can be distilled into smaller models, reducing the computational cost of alignment. We establish a new state-of-the-art performance in zero-shot settings for generative models, achieving a 2.1\% improvement on Reward Bench. Furthermore, alignment performed on the CARMO-curated preference dataset achieves 22.5\% and 21.1\% LC-WR and WR, respectively, on Mistral-Base (7B).

Integral reinforcement learning (IntRL) demands the precise computation of the utility function's integral at its policy evaluation (PEV) stage. This is achieved through quadrature rules, which are weighted sums of utility functions evaluated from state samples obtained in discrete time. Our research reveals a critical yet underexplored phenomenon: the choice of the computational method -- in this case, the quadrature rule -- can significantly impact control performance. This impact is traced back to the fact that computational errors introduced in the PEV stage can affect the policy iteration's convergence behavior, which in turn affects the learned controller. To elucidate how computation impacts control, we draw a parallel between IntRL's policy iteration and Newton's method applied to the Hamilton-Jacobi-Bellman equation. In this light, computational error in PEV manifests as an extra error term in each iteration of Newton's method, with its upper bound proportional to the computational error. Further, we demonstrate that when the utility function resides in a reproducing kernel Hilbert space (RKHS), the optimal quadrature is achievable by employing Bayesian quadrature with the RKHS-inducing kernel function. We prove that the local convergence rates for IntRL using the trapezoidal rule and Bayesian quadrature with a Mat\'ern kernel to be O(N^{-2}) and O(N^{-b}), where N is the number of evenly-spaced samples and b is the Mat\'ern kernel's smoothness parameter. These theoretical findings are finally validated by two canonical control tasks.

Aligning large language models with human objectives is paramount, yet common approaches including RLHF suffer from unstable and resource-intensive training. In response to this challenge, we introduce ARGS, Alignment as Reward-Guided Search, a novel framework that integrates alignment into the decoding process, eliminating the need for expensive RL training. By adjusting the model's probabilistic predictions using a reward signal, ARGS generates texts with semantic diversity while being aligned with human preferences, offering a promising and flexible solution for aligning language models. Notably, ARGS demonstrates consistent enhancements in average reward compared to baselines across diverse alignment tasks and various model dimensions. For example, under the same greedy-based decoding strategy, our method improves the average reward by 19.56% relative to the baseline and secures a preference or tie score of 64.33% in GPT-4 evaluation. We believe that our framework, emphasizing decoding-time alignment, paves the way for more responsive language models in the future. Code is publicly available at: https://github.com/deeplearning-wisc/args.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training language models (LMs) on reasoning tasks that elicit emergent long chains of thought (CoTs). Unlike supervised learning, it updates the model using both correct and incorrect samples via policy gradients. To better understand its mechanism, we decompose the learning signal into reinforcing correct responses and penalizing incorrect ones, referred to as Positive and Negative Sample Reinforcement (PSR and NSR), respectively. We train Qwen2.5-Math-7B and Qwen3-4B on a mathematical reasoning dataset and uncover a surprising result: training with only negative samples -- without reinforcing correct responses -- can be highly effective: it consistently improves performance over the base model across the entire Pass@k spectrum (k up to 256), often matching or surpassing PPO and GRPO. In contrast, reinforcing only correct responses improves Pass@1 but degrades performance at higher k, due to reduced diversity. These inference-scaling trends highlight that solely penalizing incorrect responses may contribute more to performance than previously recognized. Through gradient analysis, we show that NSR works by suppressing incorrect generations and redistributing probability mass toward other plausible candidates, guided by the model's prior beliefs. It refines the model's existing knowledge rather than introducing entirely new behaviors. Building on this insight, we propose a simple variant of the RL objective that upweights NSR, and show that it consistently improves overall Pass@k performance on MATH, AIME 2025, and AMC23. Our code is available at https://github.com/TianHongZXY/RLVR-Decomposed.

The success of Large Language Models (LLMs) has sparked interest in various agentic applications. A key hypothesis is that LLMs, leveraging common sense and Chain-of-Thought (CoT) reasoning, can effectively explore and efficiently solve complex domains. However, LLM agents have been found to suffer from sub-optimal exploration and the knowing-doing gap, the inability to effectively act on knowledge present in the model. In this work, we systematically study why LLMs perform sub-optimally in decision-making scenarios. In particular, we closely examine three prevalent failure modes: greediness, frequency bias, and the knowing-doing gap. We propose mitigation of these shortcomings by fine-tuning via Reinforcement Learning (RL) on self-generated CoT rationales. Our experiments across multi-armed bandits, contextual bandits, and Tic-tac-toe, demonstrate that RL fine-tuning enhances the decision-making abilities of LLMs by increasing exploration and narrowing the knowing-doing gap. Finally, we study both classic exploration mechanisms, such as epsilon-greedy, and LLM-specific approaches, such as self-correction and self-consistency, to enable more effective fine-tuning of LLMs for decision-making.

Aiming to produce reinforcement learning (RL) policies that are human-interpretable and can generalize better to novel scenarios, Trivedi et al. (2021) present a method (LEAPS) that first learns a program embedding space to continuously parameterize diverse programs from a pre-generated program dataset, and then searches for a task-solving program in the learned program embedding space when given a task. Despite the encouraging results, the program policies that LEAPS can produce are limited by the distribution of the program dataset. Furthermore, during searching, LEAPS evaluates each candidate program solely based on its return, failing to precisely reward correct parts of programs and penalize incorrect parts. To address these issues, we propose to learn a meta-policy that composes a series of programs sampled from the learned program embedding space. By learning to compose programs, our proposed hierarchical programmatic reinforcement learning (HPRL) framework can produce program policies that describe out-of-distributionally complex behaviors and directly assign credits to programs that induce desired behaviors. The experimental results in the Karel domain show that our proposed framework outperforms baselines. The ablation studies confirm the limitations of LEAPS and justify our design choices.

Personalized treatment effect estimates are often of interest in high-stakes applications -- thus, before deploying a model estimating such effects in practice, one needs to be sure that the best candidate from the ever-growing machine learning toolbox for this task was chosen. Unfortunately, due to the absence of counterfactual information in practice, it is usually not possible to rely on standard validation metrics for doing so, leading to a well-known model selection dilemma in the treatment effect estimation literature. While some solutions have recently been investigated, systematic understanding of the strengths and weaknesses of different model selection criteria is still lacking. In this paper, instead of attempting to declare a global `winner', we therefore empirically investigate success- and failure modes of different selection criteria. We highlight that there is a complex interplay between selection strategies, candidate estimators and the data used for comparing them, and provide interesting insights into the relative (dis)advantages of different criteria alongside desiderata for the design of further illuminating empirical studies in this context.

In this paper, we propose an enhanced approach for Rapid Exploration and eXploitation for AI Agents called REX. Existing AutoGPT-style techniques have inherent limitations, such as a heavy reliance on precise descriptions for decision-making, and the lack of a systematic approach to leverage try-and-fail procedures akin to traditional Reinforcement Learning (RL). REX introduces an additional layer of rewards and integrates concepts similar to Upper Confidence Bound (UCB) scores, leading to more robust and efficient AI agent performance. This approach has the advantage of enabling the utilization of offline behaviors from logs and allowing seamless integration with existing foundation models while it does not require any model fine-tuning. Through comparative analysis with existing methods such as Chain-of-Thoughts(CoT) and Reasoning viA Planning(RAP), REX-based methods demonstrate comparable performance and, in certain cases, even surpass the results achieved by these existing techniques. Notably, REX-based methods exhibit remarkable reductions in execution time, enhancing their practical applicability across a diverse set of scenarios.

Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI O1/O3 and Deepseek R1. In this work, we investigate the entire posttraining of ATP, aiming to align it with breakthroughs in reasoning models in natural languages.To begin, we continual train current ATP models with a hybrid dataset, which consists of numerous statement-proof pairs, and additional data aimed at incorporating cognitive behaviors that emulate human reasoning and hypothesis refinement. Next, we explore reinforcement learning with the use of outcome reward returned by Lean 4 compiler. Through our designed continual training and reinforcement learning processes, we have successfully improved existing formal provers, including both DeepSeek-Prover-v1.5 and Goedel-Prover, achieving state-of-the-art performance in the field of whole-proof generation. For example, we achieve a 59.8% pass rate (pass@32) on MiniF2F. This is an on-going project and we will progressively update our findings, release our data and training details.

Reinforcement Learning with Human Feedback (RLHF) and its variants have made huge strides toward the effective alignment of large language models (LLMs) to follow instructions and reflect human values. More recently, Direct Alignment Algorithms (DAAs) have emerged in which the reward modeling stage of RLHF is skipped by characterizing the reward directly as a function of the policy being learned. Examples include Direct Preference Optimization (DPO) and Simple Preference Optimization (SimPO). These methods often suffer from likelihood displacement, a phenomenon by which the probabilities of preferred responses are often reduced undesirably. In this paper, we argue that, for DAAs the reward (function) shape matters. We introduce AlphaPO, a new DAA method that leverages an alpha-parameter to help change the shape of the reward function beyond the standard log reward. AlphaPO helps maintain fine-grained control over likelihood displacement and over-optimization. Compared to SimPO, one of the best performing DAAs, AlphaPO leads to about 7\% to 10\% relative improvement in alignment performance for the instruct versions of Mistral-7B and Llama3-8B. The analysis and results presented highlight the importance of the reward shape, and how one can systematically change it to affect training dynamics, as well as improve alignment performance.

Large Language Models (LLMs) have demonstrated impressive capabilities in complex reasoning tasks, yet they still struggle to reliably verify the correctness of their own outputs. Existing solutions to this verification challenge often depend on separate verifier models or require multi-stage self-correction training pipelines, which limit scalability. In this paper, we propose Policy as Generative Verifier (PAG), a simple and effective framework that empowers LLMs to self-correct by alternating between policy and verifier roles within a unified multi-turn reinforcement learning (RL) paradigm. Distinct from prior approaches that always generate a second attempt regardless of model confidence, PAG introduces a selective revision mechanism: the model revises its answer only when its own generative verification step detects an error. This verify-then-revise workflow not only alleviates model collapse but also jointly enhances both reasoning and verification abilities. Extensive experiments across diverse reasoning benchmarks highlight PAG's dual advancements: as a policy, it enhances direct generation and self-correction accuracy; as a verifier, its self-verification outperforms self-consistency.

We consider the task of mapping pseudocode to long programs that are functionally correct. Given test cases as a mechanism to validate programs, we search over the space of possible translations of the pseudocode to find a program that passes the validation. However, without proper credit assignment to localize the sources of program failures, it is difficult to guide search toward more promising programs. We propose to perform credit assignment based on signals from compilation errors, which constitute 88.7% of program failures. Concretely, we treat the translation of each pseudocode line as a discrete portion of the program, and whenever a synthesized program fails to compile, an error localization method tries to identify the portion of the program responsible for the failure. We then focus search over alternative translations of the pseudocode for those portions. For evaluation, we collected the SPoC dataset (Search-based Pseudocode to Code) containing 18,356 programs with human-authored pseudocode and test cases. Under a budget of 100 program compilations, performing search improves the synthesis success rate over using the top-one translation of the pseudocode from 25.6% to 44.7%.

LLM-based (Large Language Model) GUI (Graphical User Interface) agents can potentially reshape our daily lives significantly. However, current LLM-based GUI agents suffer from the scarcity of high-quality training data owing to the difficulties of trajectory collection and reward annotation. Existing works have been exploring LLMs to collect trajectories for imitation learning or to offer reward signals for online RL training. However, the Outcome Reward Model (ORM) used in existing works cannot provide finegrained feedback and can over-penalize the valuable steps in finally failed trajectories. To this end, we propose Progress Reward Model (ProgRM) to provide dense informative intermediate rewards by predicting a task completion progress for each step in online training. To handle the challenge of progress reward label annotation, we further design an efficient LCS-based (Longest Common Subsequence) self-annotation algorithm to discover the key steps in trajectories and assign progress labels accordingly. ProgRM is evaluated with extensive experiments and analyses. Actors trained with ProgRM outperform leading proprietary LLMs and ORM-trained actors, illustrating the effectiveness of ProgRM. The codes for experiments will be made publicly available upon acceptance.

Risk-sensitive reinforcement learning (RL) aims to optimize policies that balance the expected reward and risk. In this paper, we present a novel risk-sensitive RL framework that employs an Iterated Conditional Value-at-Risk (CVaR) objective under both linear and general function approximations, enriched by human feedback. These new formulations provide a principled way to guarantee safety in each decision making step throughout the control process. Moreover, integrating human feedback into risk-sensitive RL framework bridges the gap between algorithmic decision-making and human participation, allowing us to also guarantee safety for human-in-the-loop systems. We propose provably sample-efficient algorithms for this Iterated CVaR RL and provide rigorous theoretical analysis. Furthermore, we establish a matching lower bound to corroborate the optimality of our algorithms in a linear context.

We introduce DeepSeek-Prover-V1.5, an open-source language model designed for theorem proving in Lean 4, which enhances DeepSeek-Prover-V1 by optimizing both training and inference processes. Pre-trained on DeepSeekMath-Base with specialization in formal mathematical languages, the model undergoes supervised fine-tuning using an enhanced formal theorem proving dataset derived from DeepSeek-Prover-V1. Further refinement is achieved through reinforcement learning from proof assistant feedback (RLPAF). Beyond the single-pass whole-proof generation approach of DeepSeek-Prover-V1, we propose RMaxTS, a variant of Monte-Carlo tree search that employs an intrinsic-reward-driven exploration strategy to generate diverse proof paths. DeepSeek-Prover-V1.5 demonstrates significant improvements over DeepSeek-Prover-V1, achieving new state-of-the-art results on the test set of the high school level miniF2F benchmark (63.5%) and the undergraduate level ProofNet benchmark (25.3%).

We study the incentivized information acquisition problem, where a principal hires an agent to gather information on her behalf. Such a problem is modeled as a Stackelberg game between the principal and the agent, where the principal announces a scoring rule that specifies the payment, and then the agent then chooses an effort level that maximizes her own profit and reports the information. We study the online setting of such a problem from the principal's perspective, i.e., designing the optimal scoring rule by repeatedly interacting with the strategic agent. We design a provably sample efficient algorithm that tailors the UCB algorithm (Auer et al., 2002) to our model, which achieves a sublinear T^{2/3}-regret after T iterations. Our algorithm features a delicate estimation procedure for the optimal profit of the principal, and a conservative correction scheme that ensures the desired agent's actions are incentivized. Furthermore, a key feature of our regret bound is that it is independent of the number of states of the environment.

Reinforcement learning exhibits potential in enhancing the reasoning abilities of large language models, yet it is hard to scale for the low sample efficiency during the rollout phase. Existing methods attempt to improve efficiency by scheduling problems based on problem difficulties. However, these approaches suffer from unstable and biased estimations of problem difficulty and fail to capture the alignment between model competence and problem difficulty in RL training, leading to suboptimal results. To tackle these limitations, this paper introduces Competence-Difficulty Alignment Sampling (CDAS), which enables accurate and stable estimation of problem difficulties by aggregating historical performance discrepancies of problems. Then the model competence is quantified to adaptively select problems whose difficulty is in alignment with the model's current competence using a fixed-point system. Experimental results across a range of challenging mathematical benchmarks show that CDAS achieves great improvements in both accuracy and efficiency. CDAS attains the highest average accuracy against baselines and exhibits significant speed advantages compared to Dynamic Sampling, a competitive strategy in DAPO, which is 2.33 times slower than CDAS.

In the absence of extensive human-annotated data for complex reasoning tasks, self-improvement -- where models are trained on their own outputs -- has emerged as a primary method for enhancing performance. However, the critical factors underlying the mechanism of these iterative self-improving methods remain poorly understood, such as under what conditions self-improvement is effective, and what are the bottlenecks in the current iterations. In this work, we identify and propose methods to monitor two pivotal factors in this iterative process: (1) the model's ability to generate sufficiently diverse responses (exploration); and (2) the effectiveness of external rewards in distinguishing high-quality candidates from lower-quality ones (exploitation). Using mathematical reasoning as a case study, we begin with a quantitative analysis to track the dynamics of exploration and exploitation, discovering that a model's exploratory capabilities rapidly deteriorate over iterations, and the effectiveness of exploiting external rewards diminishes as well. Motivated by these findings, we introduce B-STaR, a Self-Taught Reasoning framework that autonomously adjusts configurations across iterations to Balance exploration and exploitation, thereby optimizing the self-improving effectiveness based on the current policy model and available rewards. Our experiments on mathematical reasoning, coding, and commonsense reasoning demonstrate that B-STaR not only enhances the model's exploratory capabilities throughout training but also achieves a more effective balance between exploration and exploitation, leading to superior performance.

Language models (LMs) are susceptible to in-context reward hacking, where they exploit flaws in tainted or faulty written specifications or rubrics to achieve high scores without fulfilling the user's true intent. We introduce Specification Self-Correction (SSC), a novel, test-time framework that enables an LM to identify and correct flaws within its own guiding specification. SSC employs a multi-step inference process where the model first generates a response based on a potentially tainted specification, critiques its output, and then revises the specification itself to remove the exploitable loophole. A final, more robust response is then generated using this self-corrected specification. Across experiments spanning creative writing and agentic coding tasks with several LMs, we demonstrate that while models initially game tainted specifications in 50-70\% of cases, the SSC process reduces this vulnerability by over 90\%. This dynamic repair occurs at inference time, requires no weight modification, and leads to more robustly aligned model behavior. Code at https://github.com/vicgalle/specification-self-correction .

This paper studies reinforcement learning from human feedback (RLHF) for aligning large language models with human preferences. While RLHF has demonstrated promising results, many algorithms are highly sensitive to misspecifications in the underlying preference model (e.g., the Bradley-Terry model), the reference policy, or the reward function, resulting in undesirable fine-tuning. To address model misspecification, we propose a doubly robust preference optimization algorithm that remains consistent when either the preference model or the reference policy is correctly specified (without requiring both). Our proposal demonstrates superior and more robust performance than state-of-the-art algorithms, both in theory and in practice. The code is available at https://github.com/DRPO4LLM/DRPO4LLM

Despite the promise of RLHF in aligning LLMs with human preferences, it often leads to superficial alignment, prioritizing stylistic changes over improving downstream performance of LLMs. Underspecified preferences could obscure directions to align the models. Lacking exploration restricts identification of desirable outputs to improve the models. To overcome these challenges, we propose a novel framework: Reinforcement Learning from Reflective Feedback (RLRF), which leverages fine-grained feedback based on detailed criteria to improve the core capabilities of LLMs. RLRF employs a self-reflection mechanism to systematically explore and refine LLM responses, then fine-tuning the models via a RL algorithm along with promising responses. Our experiments across Just-Eval, Factuality, and Mathematical Reasoning demonstrate the efficacy and transformative potential of RLRF beyond superficial surface-level adjustment.

Reinforcement learning from human feedback (RLHF) is the mainstream paradigm used to align large language models (LLMs) with human preferences. Yet existing RLHF heavily relies on accurate and informative reward models, which are vulnerable and sensitive to noise from various sources, e.g. human labeling errors, making the pipeline fragile. In this work, we improve the effectiveness of the reward model by introducing a penalty term on the reward, named as contrastive rewards. %Contrastive rewards Our approach involves two steps: (1) an offline sampling step to obtain responses to prompts that serve as baseline calculation and (2) a contrastive reward calculated using the baseline responses and used in the Proximal Policy Optimization (PPO) step. We show that contrastive rewards enable the LLM to penalize reward uncertainty, improve robustness, encourage improvement over baselines, calibrate according to task difficulty, and reduce variance in PPO. We show empirically contrastive rewards can improve RLHF substantially, evaluated by both GPTs and humans, and our method consistently outperforms strong baselines.

Training large-scale language models is increasingly critical in various domains, but it is hindered by frequent failures, leading to significant time and economic costs. Current failure recovery methods in cloud-based settings inadequately address the diverse and complex scenarios that arise, focusing narrowly on erasing downtime for individual tasks without considering the overall cost impact on a cluster. We introduce Unicron, a workload manager designed for efficient self-healing in large-scale language model training. Unicron optimizes the training process by minimizing failure-related costs across multiple concurrent tasks within a cluster. Its key features include in-band error detection for real-time error identification without extra overhead, a dynamic cost-aware plan generation mechanism for optimal reconfiguration, and an efficient transition strategy to reduce downtime during state changes. Deployed on a 128-GPU distributed cluster, Unicron demonstrates up to a 1.9x improvement in training efficiency over state-of-the-art methods, significantly reducing failure recovery costs and enhancing the reliability of large-scale language model training.