Finite-Time Analysis of Natural Actor-Critic for POMDPs

TL;DR

This paper proves the first non-asymptotic convergence results for actor-critic algorithms applied to POMDPs with finite memory, addressing challenges of partial observability and function approximation.

Contribution

It introduces a finite-time analysis of actor-critic methods for POMDPs, explicitly quantifying errors from finite-state controllers and demonstrating how larger controllers reduce this error.

Findings

First non-asymptotic convergence proof for POMDP actor-critic.

Explicit error bounds related to finite-state controllers.

Larger block sizes in controllers reduce approximation error.

Abstract

We consider the reinforcement learning problem for partially observed Markov decision processes (POMDPs) with large or even countably infinite state spaces, where the controller has access to only noisy observations of the underlying controlled Markov chain. We consider a natural actor-critic method that employs a finite internal memory for policy parameterization, and a multi-step temporal difference learning algorithm for policy evaluation. We establish, to the best of our knowledge, the first non-asymptotic global convergence of actor-critic methods for partially observed systems under function approximation. In particular, in addition to the function approximation and statistical errors that also arise in MDPs, we explicitly characterize the error due to the use of finite-state controllers. This additional error is stated in terms of the total variation distance between the traditional belief state in POMDPs and the posterior distribution of the hidden state when using a finite-state controller. Further, we show that this error can be made small in the case of sliding-block controllers by using larger block sizes.