Performance Bounds for Policy-Based Average Reward Reinforcement Learning Algorithms

TL;DR

This paper establishes the first finite-time error bounds for policy-based average reward reinforcement learning algorithms, demonstrating that errors diminish as evaluation and improvement errors decrease.

Contribution

It provides the first finite-time performance bounds for average reward RL algorithms, addressing a long-standing open problem in the field.

Findings

Finite-time error bounds for average reward MDPs are derived.

Asymptotic error approaches zero with improved policy evaluation and improvement.

Addresses the challenge of unbounded bounds in average reward RL with near-1 discount factors.

Abstract

Many policy-based reinforcement learning (RL) algorithms can be viewed as instantiations of approximate policy iteration (PI), i.e., where policy improvement and policy evaluation are both performed approximately. In applications where the average reward objective is the meaningful performance metric, discounted reward formulations are often used with the discount factor being close to $1,$ which is equivalent to making the expected horizon very large. However, the corresponding theoretical bounds for error performance scale with the square of the horizon. Thus, even after dividing the total reward by the length of the horizon, the corresponding performance bounds for average reward problems go to infinity. Therefore, an open problem has been to obtain meaningful performance bounds for approximate PI and RL algorithms for the average-reward setting. In this paper, we solve this open problem by obtaining the first finite-time error bounds for average-reward MDPs, and show that the asymptotic error goes to zero in the limit as policy evaluation and policy improvement errors go to zero.