Infinite-Horizon Policy-Gradient Estimation

TL;DR

This paper introduces GPOMDP, a simulation-based algorithm for estimating the gradient of average reward in POMDPs, requiring minimal storage, no knowledge of the underlying state, and offering convergence guarantees.

Contribution

The paper presents GPOMDP, a novel biased gradient estimation algorithm for POMDPs that is simple, efficient, and provably convergent, with extensions to various complex settings.

Findings

GPOMDP requires only twice the number of policy parameters in storage.

The bias-variance trade-off controlled by parameter β affects convergence.

The algorithm converges under certain mixing time conditions.

Abstract

Gradient-based approaches to direct policy search in reinforcement learning have received much recent attention as a means to solve problems of partial observability and to avoid some of the problems associated with policy degradation in value-function methods. In this paper we introduce GPOMDP, a simulation-based algorithm for generating a {\em biased} estimate of the gradient of the {\em average reward} in Partially Observable Markov Decision Processes (POMDPs) controlled by parameterized stochastic policies. A similar algorithm was proposed by Kimura, Yamamura, and Kobayashi (1995). The algorithm's chief advantages are that it requires storage of only twice the number of policy parameters, uses one free parameter $\beta\in [0,1)$ (which has a natural interpretation in terms of bias-variance trade-off), and requires no knowledge of the underlying state. We prove convergence of GPOMDP, and show how the correct choice of the parameter $\beta$ is related to the {\em mixing time} of the controlled POMDP. We briefly describe extensions of GPOMDP to controlled Markov chains, continuous state, observation and control spaces, multiple-agents, higher-order derivatives, and a version for training stochastic policies with internal states. In a companion paper (Baxter, Bartlett, & Weaver, 2001) we show how the gradient estimates generated by GPOMDP can be used in both a traditional stochastic gradient algorithm and a conjugate-gradient procedure to find local optima of the average reward