A Finite Time Analysis of Two Time-Scale Actor Critic Methods

TL;DR

This paper provides the first finite-time analysis and sample complexity bounds for two time-scale actor-critic methods in reinforcement learning, demonstrating convergence to a stationary point within a specified sample complexity.

Contribution

It offers the first non-asymptotic convergence analysis and finite sample complexity bounds for two time-scale actor-critic algorithms under non-i.i.d. conditions.

Findings

Guarantees convergence to a first-order stationary point

Achieves a sample complexity of rac{( heta)}{}( ext{ ilde{O}}(^{-2.5}))

First work to establish finite-time bounds for these methods

Abstract

Actor-critic (AC) methods have exhibited great empirical success compared with other reinforcement learning algorithms, where the actor uses the policy gradient to improve the learning policy and the critic uses temporal difference learning to estimate the policy gradient. Under the two time-scale learning rate schedule, the asymptotic convergence of AC has been well studied in the literature. However, the non-asymptotic convergence and finite sample complexity of actor-critic methods are largely open. In this work, we provide a non-asymptotic analysis for two time-scale actor-critic methods under non-i.i.d. setting. We prove that the actor-critic method is guaranteed to find a first-order stationary point (i.e., $\|\nabla J(\boldsymbol{\theta})\|_2^2 \le \epsilon$) of the non-concave performance function $J(\boldsymbol{\theta})$, with $\mathcal{\tilde{O}}(\epsilon^{-2.5})$ sample complexity. To the best of our knowledge, this is the first work providing finite-time analysis and sample complexity bound for two time-scale actor-critic methods.