Regret Analysis of Policy Gradient Algorithm for Infinite Horizon Average Reward Markov Decision Processes

TL;DR

This paper introduces a novel policy gradient algorithm for infinite horizon average reward MDPs, demonstrating its global convergence and establishing a regret bound of O(T^{3/4}) in a pioneering study.

Contribution

It presents the first regret analysis for a general policy gradient algorithm in average reward MDPs without assuming linear structure.

Findings

Proposed algorithm converges globally.

Achieves O(T^{3/4}) regret bound.

First regret analysis for general policy gradient in this setting.

Abstract

In this paper, we consider an infinite horizon average reward Markov Decision Process (MDP). Distinguishing itself from existing works within this context, our approach harnesses the power of the general policy gradient-based algorithm, liberating it from the constraints of assuming a linear MDP structure. We propose a policy gradient-based algorithm and show its global convergence property. We then prove that the proposed algorithm has $\tilde{\mathcal{O}}({T}^{3/4})$ regret. Remarkably, this paper marks a pioneering effort by presenting the first exploration into regret-bound computation for the general parameterized policy gradient algorithm in the context of average reward scenarios.