Policy Improvement for POMDPs Using Normalized Importance Sampling

TL;DR

This paper introduces a new biased but low-variance estimator for evaluating policies in POMDPs using normalized importance sampling, enabling efficient policy improvement without prior knowledge of the environment.

Contribution

The paper proposes a novel normalized importance sampling estimator for POMDP policy evaluation that is unbiased in theory but practically biased with low variance, improving sample efficiency.

Findings

Estimator has low variance and is effective for pair-wise policy comparisons.

Extends to policies with memory, broadening applicability.

Achieves an order of magnitude reduction in trials compared to REINFORCE.

Abstract

We present a new method for estimating the expected return of a POMDP from experience. The method does not assume any knowledge of the POMDP and allows the experience to be gathered from an arbitrary sequence of policies. The return is estimated for any new policy of the POMDP. We motivate the estimator from function-approximation and importance sampling points-of-view and derive its theoretical properties. Although the estimator is biased, it has low variance and the bias is often irrelevant when the estimator is used for pair-wise comparisons. We conclude by extending the estimator to policies with memory and compare its performance in a greedy search algorithm to REINFORCE algorithms showing an order of magnitude reduction in the number of trials required.