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

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 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(), and off-policy TD algorithms including V-trace. As a by-product, by analyzing the convergence bounds of n-step TD and TD(), 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).

Tasks

Reproductions