Algorithms and Bounds for Rollout Sampling Approximate Policy Iteration

TL;DR

This paper analyzes sample complexity in approximate policy iteration using classifiers, comparing uniform and adaptive rollout sampling strategies over discretized state spaces to improve efficiency.

Contribution

It introduces and compares a simple adaptive sampling method to uniform sampling in policy iteration, reducing sample complexity in continuous state spaces.

Findings

Adaptive sampling requires fewer samples than uniform sampling.

Discretized grid covering scheme is effective for continuous state spaces.

Sample complexity can be significantly reduced with targeted sampling.

Abstract

Several approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a supervised learning problem, have been proposed recently. Finding good policies with such methods requires not only an appropriate classifier, but also reliable examples of best actions, covering the state space sufficiently. Up to this time, little work has been done on appropriate covering schemes and on methods for reducing the sample complexity of such methods, especially in continuous state spaces. This paper focuses on the simplest possible covering scheme (a discretized grid over the state space) and performs a sample-complexity comparison between the simplest (and previously commonly used) rollout sampling allocation strategy, which allocates samples equally at each state under consideration, and an almost as simple method, which allocates samples only as needed and requires significantly fewer samples.