A priori Estimates for Deep Residual Network in Continuous-time Reinforcement Learning

Deep reinforcement learning excels in numerous large-scale practical applications. However, existing performance analyses ignores the unique characteristics of continuous-time control problems, is unable to directly estimate the generalization error of the Bellman optimal loss and require a boundedness assumption. Our work focuses on continuous-time control problems and proposes a method that is applicable to all such problems where the transition function satisfies semi-group and Lipschitz properties. Under this method, we can directly analyze the \emph{a priori} generalization error of the Bellman optimal loss. The core of this method lies in two transformations of the loss function. To complete the transformation, we propose a decomposition method for the maximum operator. Additionally, this analysis method does not require a boundedness assumption. Finally, we obtain an \emph{a priori} generalization error without the curse of dimensionality.

A prior Estimates for Deep Residual Network in Continuous-time Reinforcement Learning

Deep reinforcement learning excels in numerous large-scale practical applications. However, existing performance analyses ignores the unique characteristics of continuous-time control problems, is unable to directly estimate the generalization error of the Bellman optimal loss and require a boundedness assumption. Our work focuses on continuous-time control problems and proposes a method that is applicable to all such problems where the transition function satisfies semi-group and Lipschitz properties. Under this method, we can directly analyze the \emph{a priori} generalization error of the Bellman optimal loss. The core of this method lies in two transformations of the loss function. To complete the transformation, we propose a decomposition method for the maximum operator. Additionally, this analysis method does not require a boundedness assumption. Finally, we obtain an \emph{a priori} generalization error without the curse of dimensionality.

An Experimental Comparison Between Temporal Difference and Residual Gradient with Neural Network Approximation

Gradient descent or its variants are popular in training neural networks. However, in deep Q-learning with neural network approximation, a type of reinforcement learning, gradient descent (also known as Residual Gradient (RG)) is barely used to solve Bellman residual minimization problem. On the contrary, Temporal Difference (TD), an incomplete gradient descent method prevails. In this work, we perform extensive experiments to show that TD outperforms RG, that is, when the training leads to a small Bellman residual error, the solution found by TD has a better policy and is more robust against the perturbation of neural network parameters. We further use experiments to reveal a key difference between reinforcement learning and supervised learning, that is, a small Bellman residual error can correspond to a bad policy in reinforcement learning while the test loss function in supervised learning is a standard index to indicate the performance. We also empirically examine that the missing term in TD is a key reason why RG performs badly. Our work shows that the performance of a deep Q-learning solution is closely related to the training dynamics and how an incomplete gradient descent method can find a good policy is interesting for future study.

FoldingZero: Protein Folding from Scratch in Hydrophobic-Polar Model

De novo protein structure prediction from amino acid sequence is one of the most challenging problems in computational biology. As one of the extensively explored mathematical models for protein folding, Hydrophobic-Polar (HP) model enables thorough investigation of protein structure formation and evolution. Although HP model discretizes the conformational space and simplifies the folding energy function, it has been proven to be an NP-complete problem. In this paper, we propose a novel protein folding framework FoldingZero, self-folding a de novo protein 2D HP structure from scratch based on deep reinforcement learning. FoldingZero features the coupled approach of a two-head (policy and value heads) deep convolutional neural network (HPNet) and a regularized Upper Confidence Bounds for Trees (R-UCT). It is trained solely by a reinforcement learning algorithm, which improves HPNet and R-UCT iteratively through iterative policy optimization. Without any supervision and domain knowledge, FoldingZero not only achieves comparable results, but also learns the latent folding knowledge to stabilize the structure. Without exponential computation, FoldingZero shows promising potential to be adopted for real-world protein properties prediction.