论文检索

Reinforcement Learning/Function Approximation

Jiaming Guo, Rui Zhang, Shaohui Peng, Qi Yi, Xing Hu, Ruizhi Chen, Zidong Du, xishan zhang, Ling Li, Qi Guo 等

Deep reinforcement learning (DRL) has led to a wide range of advances in sequential decision-making tasks. However, the complexity of neural network policies makes it difficult to understand and deploy with limited computational resources. Currently, employing compact symbolic expressions as symbolic policies is a promising strategy to obtain simple and interpretable policies. Previous symbolic policy methods usually involve complex training processes and pre-trained neural network policies, which are inefficient and limit the application of symbolic policies. In this paper, we propose an efficient gradient-based learning method named Efficient Symbolic Policy Learning (ESPL) that learns the symbolic policy from scratch in an end-to-end way. We introduce a symbolic network as the search space and employ a path selector to find the compact symbolic policy. By doing so we represent the policy with a differentiable symbolic expression and train it in an off-policy manner which further improves the efficiency. In addition, in contrast with previous symbolic policies which only work in single-task RL because of complexity, we expand ESPL on meta-RL to generate symbolic policies for unseen tasks. Experimentally, we show that our approach generates symbolic policies with higher performance and greatly improves data efficiency for single-task RL. In meta-RL, we demonstrate that compared with neural network policies the proposed symbolic policy achieves higher performance and efficiency and shows the potential to be interpretable.

Reinforcement Learning/Function Approximation

Sattar Vakili, Julia Olkhovskaya

Modern reinforcement learning (RL) has shown empirical success in various real world settings with complex models and large state-action spaces. The existing analytical results, however, typically focus on settings with a small number of state-actions or simple models such as linearly modeled state-action value functions. To derive RL policies that efficiently handle large state-action spaces with more general value functions, some recent works have considered nonlinear function approximation using kernel ridge regression. We propose $\pi$-KRVI, an optimistic modification of least-squares value iteration, when the action-value function is represented by an RKHS. We prove the first order-optimal regret guarantees under a general setting. Our results show a significant polynomial in the number of episodes improvement over the state of the art. In particular, with highly non-smooth kernels (such as Neural Tangent kernel or some Matérn kernels) the existing results lead to trivial (superlinear in the number of episodes) regret bounds. We show a sublinear regret bound that is order optimal in the cases where a lower bound on regret is known (which includes the kernels mentioned above).

Reinforcement Learning/Function Approximation

Zak Mhammedi, Adam Block, Dylan J Foster, Alexander Rakhlin

A major challenge in reinforcement learning is to develop practical, sample-efficient algorithms for exploration in high-dimensional domains where generalization and function approximation is required. Low-Rank Markov Decision Processes---where transition probabilities admit a low-rank factorization based on an unknown feature embedding---offer a simple, yet expressive framework for RL with function approximation, yet existing algorithms either (1) are computationally intractable, or (2) require restrictive statistical assumptions such as latent variable structure or access to model-based function approximation. In this work, we propose the first provably sample-efficient algorithm for exploration in Low-Rank MDPs that is both computationally efficient and model-free, allowing for general function approximation while requiring no structural assumptions beyond a reachability condition that we show is substantially weaker than that assumed in prior work. Our algorithm, SpanRL, uses the notion of a barycentric spanner for the feature embedding as an efficiently computable basis for exploration, performing efficient spanner computation by interleaving representation learning and policy optimization subroutines. Our analysis---which is appealingly simple and modular---carefully combines several techniques, including a new approach to error-tolerant barycentric spanner computation, and a new analysis of a certain minimax representation learning objective found in prior work.

Reinforcement Learning/Function Approximation

Andrew Wagenmaker, Guanya Shi, Kevin Jamieson

Learning to control unknown nonlinear dynamical systems is a fundamental problem in reinforcement learning and control theory. A commonly applied approach is to first explore the environment (exploration), learn an accurate model of it (system identification), and then compute an optimal controller with the minimum cost on this estimated system (policy optimization). While existing work has shown that it is possible to learn a uniformly good model of the system (Mania et al., 2020), in practice, if we aim to learn a good controller with a low cost on the actual system, certain system parameters may be significantly more critical than others, and we therefore ought to focus our exploration on learning such parameters.In this work, we consider the setting of nonlinear dynamical systems and seek to formally quantify, in such settings, (a) which parameters are most relevant to learning a good controller, and (b) how we can best explore so as to minimize uncertainty in such parameters. Inspired by recent work in linear systems (Wagenmaker et al., 2021), we show that minimizing the controller loss in nonlinear systems translates to estimating the system parameters in a particular, task-dependent metric. Motivated by this, we develop an algorithm able to efficiently explore the system to reduce uncertainty in this metric, and prove a lower bound showing that our approach learns a controller at a near-instance-optimal rate. Our algorithm relies on a general reduction from policy optimization to optimal experiment design in arbitrary systems, and may be of independent interest. We conclude with experiments demonstrating the effectiveness of our method in realistic nonlinear robotic systems.

Reinforcement Learning/Function Approximation

Kavosh Asadi, Shoham Sabach, Yao Liu, Omer Gottesman, Rasool Fakoor

We study the convergence behavior of the celebrated temporal-difference (TD) learning algorithm. By looking at the algorithm through the lens of optimization, we first argue that TD can be viewed as an iterative optimization algorithm where the function to be minimized changes per iteration. By carefully investigating the divergence displayed by TD on a classical counter example, we identify two forces that determine the convergent or divergent behavior of the algorithm. We next formalize our discovery in the linear TD setting with quadratic loss and prove that convergence of TD hinges on the interplay between these two forces. We extend this optimization perspective to prove convergence of TD in a much broader setting than just linear approximation and squared loss. Our results provide a theoretical explanation for the successful application of TD in reinforcement learning.

Reinforcement Learning/Function Approximation

Haoxing Tian, Alex Olshevsky, Yannis Paschalidis

The early theory of actor-critic methods considered convergence using linear function approximators for the policy and value functions. Recent work has established convergence using neural network approximators with a single hidden layer. In this work we are taking the natural next step and establish convergence using deep neural networks with an arbitrary number of hidden layers, thus closing a gap between theory and practice. We show that actor-critic updates projected on a ball around the initial condition will converge to a neighborhood where the average of the squared gradients is $\tilde{O} \left( 1/\sqrt{m} \right) + O \left( \epsilon \right)$, with $m$ being the width of the neural network and $\epsilon$ the approximation quality of the best critic neural network over the projected set.

Reinforcement Learning/Function Approximation

Kaiwen Wang, Kevin Zhou, Runzhe Wu, Nathan Kallus, Wen Sun

While distributional reinforcement learning (DistRL) has been empirically effective, the question of when and why it is better than vanilla, non-distributional RL has remained unanswered.This paper explains the benefits of DistRL through the lens of small-loss bounds, which are instance-dependent bounds that scale with optimal achievable cost.Particularly, our bounds converge much faster than those from non-distributional approaches if the optimal cost is small.As warmup, we propose a distributional contextual bandit (DistCB) algorithm, which we show enjoys small-loss regret bounds and empirically outperforms the state-of-the-art on three real-world tasks.In online RL, we propose a DistRL algorithm that constructs confidence sets using maximum likelihood estimation. We prove that our algorithm enjoys novel small-loss PAC bounds in low-rank MDPs.As part of our analysis, we introduce the $\ell_1$ distributional eluder dimension which may be of independent interest. Then, in offline RL, we show that pessimistic DistRL enjoys small-loss PAC bounds that are novel to the offline setting and are more robust to bad single-policy coverage.

Reinforcement Learning/Function Approximation

David Yu-Tung Hui, Aaron Courville, Pierre-Luc Bacon

We show that Deep Neural Networks introduce two heteroscedastic Gumbel noise sources into Q-Learning. To account for these noise sources, we propose Double Gumbel Q-Learning, a Deep Q-Learning algorithm applicable for both discrete and continuous control. In discrete control, we derive a closed-form expression for the loss function of our algorithm. In continuous control, this loss function is intractable and we therefore derive an approximation with a hyperparameter whose value regulates pessimism in Q-Learning. We present a default value for our pessimism hyperparameter that enables DoubleGum to outperform DDPG, TD3, SAC, XQL, quantile regression, and Mixture-of-Gaussian Critics in aggregate over 33 tasks from DeepMind Control, MuJoCo, MetaWorld, and Box2D and show that tuning this hyperparameter may further improve sample efficiency.

Reinforcement Learning/Function Approximation

Jincheng Mei, Bo Dai, Alekh Agarwal, Mohammad Ghavamzadeh, Csaba Szepesvari, Dale Schuurmans

We prove that, for finite-arm bandits with linear function approximation, the global convergence of policy gradient (PG) methods depends on inter-related properties between the policy update and the representation. textcolor{blue}{First}, we establish a few key observations that frame the study: \textbf{(i)} Global convergence can be achieved under linear function approximation without policy or reward realizability, both for the standard Softmax PG and natural policy gradient (NPG). \textbf{(ii)} Approximation error is not a key quantity for characterizing global convergence in either algorithm. \textbf{(iii)} The conditions on the representation that imply global convergence are different between these two algorithms. Overall, these observations call into question approximation error as an appropriate quantity for characterizing the global convergence of PG methods under linear function approximation. \textcolor{blue}{Second}, motivated by these observations, we establish new general results: \textbf{(i)} NPG with linear function approximation achieves global convergence \emph{if and only if} the projection of the reward onto the representable space preserves the optimal action's rank, a quantity that is not strongly related to approximation error. \textbf{(ii)} The global convergence of Softmax PG occurs if the representation satisfies a non-domination condition and can preserve the ranking of rewards, which goes well beyond policy or reward realizability. We provide experimental results to support these theoretical findings.