text: Abstract In recent years, attention has been focused on the relationship between black-box optimization problem and reinforcement learning problem. In this research, we propose the Mirror Descent Search (MDS) algorithm which is applicable both for black box optimization problems and reinforcement learning problems. Our method is based on the mirror descent method, which is a general optimization algorithm. The contribution of this research is roughly twofold. We propose two essential algorithms, called MDS and Accelerated Mirror Descent Search (AMDS), and two more approximate algorithms: Gaussian Mirror Descent Search (G-MDS) and Gaussian Accelerated Mirror Descent Search (G-AMDS). This research shows that the advanced methods developed in the context of the mirror descent research can be applied to reinforcement learning problem. We also clarify the relationship between an existing reinforcement learning algorithm and our method. With two evaluation experiments, we show our proposed algorithms converge faster than some state-of-the-art methods.
  @cite_35: 
  @cite_34: Robotic learning on real hardware requires an efficient algorithm which minimizes the number of trials needed to learn an optimal policy. Prolonged use of hardware causes wear and tear on the system and demands more attention from an operator. To this end, we present a novel black-box optimization algorithm, Reward Optimization with Compact Kernels and fast natural gradient regression (ROCK∗). Our algorithm immediately updates knowledge after a single trial and is able to extrapolate in a controlled manner. These features make fast and safe learning on real hardware possible. We have evaluated our algorithm on two simulated reaching tasks of a 50 degree-of-freedom robot arm and on a hopping task of a real articulated legged system. ROCK∗ outperformed current state-of-the-art algorithms in all tasks by a factor of three or more.
  @cite_39: Reinforcement learning (RL) is one of the most general approaches to learning control. Its applicability to complex motor systems, however, has been largely impossible so far due to the computational difficulties that reinforcement learning encounters in high dimensional continuous state-action spaces. In this paper, we derive a novel approach to RL for parameterized control policies based on the framework of stochastic optimal control with path integrals. While solidly grounded in optimal control theory and estimation theory, the update equations for learning are surprisingly simple and have no danger of numerical instabilities as neither matrix inversions nor gradient learning rates are required. Empirical evaluations demonstrate significant performance improvements over gradient-based policy learning and scalability to high-dimensional control problems. Finally, a learning experiment on a robot dog illustrates the functionality of our algorithm in a real-world scenario. We believe that our new algorithm, Policy Improvement with Path Integrals (PI2), offers currently one of the most efficient, numerically robust, and easy to implement algorithms for RL in robotics.
  @cite_24: 
  @cite_16: Policy improvement methods seek to optimize the parameters of a policy with respect to a utility function. There are two main approaches to performing this optimization: reinforcement learning (RL) and black-box optimization (BBO). Whereas BBO algorithms are generic optimization methods that, due to there generality, may also be applied to optimizing policy parameters, RL algorithms are specifically tailored to leveraging the structure of policy improvement problems. In recent years, benchmark comparisons between RL and BBO have been made, and there has been several attempts to specify which approach works best for which types of problem classes. In this article, we make several contributions to this line of research: 1) We define four algorithmic properties that further clarify the relationship between RL and BBO: action-perturbation vs. parameter-perturbation, gradient estimation vs. rewardweighted averaging, use of only rewards vs. use of rewards and state information, actor-critic vs. direct policy search. 2) We show how the chronology of the derivation of ever more powerful algorithms displays a trend towards algorithms based on parameter-perturbation and reward-weighted averaging. A striking feature of this trend is that it has moved RL methods closer and closer to BBO. 3) We continue this trend by applying two modifications to the state-of-the-art "Policy Improvement with Path Integrals" (PI2), which yields an algorithm we denote PIBB. We show that PIBB is a BBO algorithm, and, more specifically, that it is a special case of the "Covariance Matrix Adaptation - Evolutionary Strategy" algorithm. Our empirical evaluation demonstrates that the simpler PIBB outperforms PI2 on simple evaluation tasks in terms of convergence speed and final cost. 4) Although our evaluation implies that, for these five tasks, BBO outperforms RL, we do not hold this to be a general statement, and provide an analysis of why these tasks are particularly well-suited for BBO. Thus, rather than making the case for BBO or RL, one of the main contributions of this article is rather to provide an algorithmic framework in which such cases may be made, as PIBB and PI2 use identical perturbation and parameter update methods, and differ only in being BBO and RL approaches respectively.
  @cite_25: This paper integrates recent work on Path Integral (PI) and Kullback Leibler (KL) divergence stochastic optimal control theory with earlier work on risk sensitivity and the fundamental dualities between free energy and relative entropy. We derive the path integral optimal control framework and its iterative version based on the aforemetioned dualities. The resulting formulation of iterative path integral control is valid for general feedback policies and in contrast to previous work, it does not rely on pre-specified policy parameterizations. The derivation is based on successive applications of Girsanov's theorem and the use of Radon-Nikodým derivative as applied to diffusion processes due to the change of measure in the stochastic dynamics. We compare the PI control derived based on Dynamic Programming with PI based on the duality between free energy and relative entropy. Moreover we extend our analysis on the applicability of the relationship between free energy and relative entropy to optimal control of markov jump diffusions processes. Furthermore, we present the links between KL stochastic optimal control and the aforementioned dualities and discuss its generalizability.
summary: PI @math @cite_39 @cite_35 would be one of the worth mentioning RL algorithm. PI @math encouraged researchers @cite_16 @cite_34 to focus on the relationship between RL algorithms and black box optimization. For example, @cite_16 proposes a reinforcement learning algorithm PI @math on the basis of black box optimization algorithm: CMA-ES. The authors @cite_25 @cite_24 discussed the connection between PI @math and KL control. We further discuss PI @math from a viewpoint of our proposed methods at section .