Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularization

TL;DR

This paper provides non-asymptotic convergence guarantees for entropy-regularized natural policy gradient methods in reinforcement learning, showing linear or quadratic convergence under certain conditions and highlighting the role of entropy in fast convergence.

Contribution

It establishes the first non-asymptotic convergence rates for entropy-regularized NPG methods with exact and inexact policy evaluation in discounted MDPs.

Findings

Converges linearly or quadratically near the optimum.

Stable convergence despite inexact policy evaluation.

Entropy regularization accelerates convergence.

Abstract

Natural policy gradient (NPG) methods are among the most widely used policy optimization algorithms in contemporary reinforcement learning. This class of methods is often applied in conjunction with entropy regularization -- an algorithmic scheme that encourages exploration -- and is closely related to soft policy iteration and trust region policy optimization. Despite the empirical success, the theoretical underpinnings for NPG methods remain limited even for the tabular setting. This paper develops $\textit{non-asymptotic}$ convergence guarantees for entropy-regularized NPG methods under softmax parameterization, focusing on discounted Markov decision processes (MDPs). Assuming access to exact policy evaluation, we demonstrate that the algorithm converges linearly -- or even quadratically once it enters a local region around the optimal policy -- when computing optimal value functions of the regularized MDP. Moreover, the algorithm is provably stable vis-\`a-vis inexactness of policy evaluation. Our convergence results accommodate a wide range of learning rates, and shed light upon the role of entropy regularization in enabling fast convergence.