text: Recently, neural networks trained as optimizers under the "learning to learn" or meta-learning framework have been shown to be effective for a broad range of optimization tasks including derivative-free black-box function optimization. Recurrent neural networks (RNNs) trained to optimize a diverse set of synthetic non-convex differentiable functions via gradient descent have been effective at optimizing derivative-free black-box functions. In this work, we propose RNN-Opt: an approach for learning RNN-based optimizers for optimizing real-parameter single-objective continuous functions under limited budget constraints. Existing approaches utilize an observed improvement based meta-learning loss function for training such models. We propose training RNN-Opt by using synthetic non-convex functions with known (approximate) optimal values by directly using discounted regret as our meta-learning loss function. We hypothesize that a regret-based loss function mimics typical testing scenarios, and would therefore lead to better optimizers compared to optimizers trained only to propose queries that improve over previous queries. Further, RNN-Opt incorporates simple yet effective enhancements during training and inference procedures to deal with the following practical challenges: i) Unknown range of possible values for the black-box function to be optimized, and ii) Practical and domain-knowledge based constraints on the input parameters. We demonstrate the efficacy of RNN-Opt in comparison to existing methods on several synthetic as well as standard benchmark black-box functions along with an anonymized industrial constrained optimization problem.
  @cite_0: Abstract This paper presents a combustion optimization system for coal-fired boilers that includes a trade-off between emissions control and boiler efficiency. Designing an optimizer for this nonlinear, multiple-input multiple-output problem is challenging. This paper describes the development of an integrated combustion optimization system called ThermalNet, which is based on a deep Q-network (DQN) and a long short-term memory (LSTM) module. ThermalNet is a highly automated system consisting of an LSTM–ConvNet predictor and a DQN optimizer. The LSTM–ConvNet extracts the features of boiler behavior from the distributed control system (DCS) operational data of a supercritical thermal plant. The DQN reinforcement learning optimizer contributes to the online development of policies based on static and dynamic states. ThermalNet establishes a sequence of control actions that both reduce emissions and simultaneously enhance fuel utilization. The internal structure of the DQN optimizer demonstrates a greater representation capacity than does the shallow multilayer optimizer. The presented experiments indicate the effectiveness of the proposed optimization system.
  @cite_16: In recent years, the large amount of labeled data available has also helped tend research toward using minimal domain knowledge, e.g., in deep neural network research. However, in many situations, data is limited and of poor quality. Can domain knowledge be useful in such a setting? In this paper, we propose domain adapted neural networks (DANN) to explore how domain knowledge can be integrated into model training for deep networks. In particular, we incorporate loss terms for knowledge available as monotonicity constraints and approximation constraints. We evaluate our model on both synthetic data generated using the popular Bohachevsky function and a real-world dataset for predicting oxygen solubility in water. In both situations, we find that our DANN model outperforms its domain-agnostic counterpart yielding an overall mean performance improvement of 19.5 with a worst- and best-case performance improvement of 4 and 42.7 , respectively.
  @cite_22: This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improve the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physical models, while generating outputs consistent with physical laws, and achieving good generalizability. Standard RNNs, even when producing superior prediction accuracy, often produce physically inconsistent results and lack generalizability. We further enhance this approach by using a pre-training method that leverages the simulated data from a physics-based model to address the scarcity of observed data. The PGRNN has the flexibility to incorporate additional physical constraints and we incorporate a density-depth relationship. Both enhancements further improve PGRNN performance. Although we present and evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where mechanistic (also known as process-based) models are used, e.g., power engineering, climate science, materials science, computational chemistry, and biomedicine.
  @cite_23: Deep reinforcement learning was employed to optimize chemical reactions. Our model iteratively records the results of a chemical reaction and chooses new experimental conditions to improve the reaction outcome. This model outperformed a state-of-the-art blackbox optimization algorithm by using 71 fewer steps on both simulations and real reactions. Furthermore, we introduced an efficient exploration strategy by drawing the reaction conditions from certain probability distributions, which resulted in an improvement on regret from 0.062 to 0.039 compared with a deterministic policy. Combining the efficient exploration policy with accelerated microdroplet reactions, optimal reaction conditions were determined in 30 min for the four reactions considered, and a better understanding of the factors that control microdroplet reactions was reached. Moreover, our model showed a better performance after training on reactions with similar or even dissimilar underlying mechanisms, which demonstrates its learning ability.
summary: Recent work on Physics-guided deep learning @cite_22 @cite_16 incorporates domain knowledge in the learning process via additional loss terms. Such approaches can be useful in our setting if the optimizer network is to be trained from scratch for a given application. However, the purpose of building a generic optimizer that can be transferred to new applications requires incorporating domain constraints in a posterior manner during inference time when the optimizer is suggesting query points. This is not only useful to adapt the same optimizer to a new application but also useful in another practical scenario of adapting to a new set of domain constraints for a given application. ThermalNet @cite_0 uses a deep Q-network as an optimizer and uses an LSTM predictor for combustion optimization of a boiler in a power plant but does not handle domain constraints. Similar to our approach, ChemOpt @cite_23 uses an RNN based optimizer for chemical reaction optimization but does not address aspects related to handling an unknown range for the function being optimized and incorporating domain constraints.