A Lyapunov Theory for Finite-Sample Guarantees of Asynchronous Q-Learning and TD-Learning Variants

• URL: http://arxiv.org/abs/2102.01567v4
• Date: Mon, 4 Sep 2023 20:15:15 GMT
• Title: A Lyapunov Theory for Finite-Sample Guarantees of Asynchronous Q-Learning and TD-Learning Variants
• Authors: Zaiwei Chen, Siva Theja Maguluri, Sanjay Shakkottai, and Karthikeyan Shanmugam
• Abstract summary: This paper develops a framework to study finite-sample convergence guarantees of a class of value-based asynchronous RL algorithms. As a by-product, we provide theoretical insights into the bias-variance trade-off, i.e., efficiency of bootstrapping in RL.
• Score: 39.28675942566465
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper develops an unified framework to study finite-sample convergence guarantees of a large class of value-based asynchronous reinforcement learning (RL) algorithms. We do this by first reformulating the RL algorithms as \textit{Markovian Stochastic Approximation} (SA) algorithms to solve fixed-point equations. We then develop a Lyapunov analysis and derive mean-square error bounds on the convergence of the Markovian SA. Based on this result, we establish finite-sample mean-square convergence bounds for asynchronous RL algorithms such as $Q$-learning, $n$-step TD, TD$(\lambda)$, and off-policy TD algorithms including V-trace. As a by-product, by analyzing the convergence bounds of $n$-step TD and TD$(\lambda)$, we provide theoretical insights into the bias-variance trade-off, i.e., efficiency of bootstrapping in RL. This was first posed as an open problem in (Sutton, 1999).

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