On the Linear convergence of Natural Policy Gradient Algorithm

TL;DR

This paper proves that Natural Policy Gradient algorithms in reinforcement learning have a linear convergence rate and introduces adaptive step size variants to enhance performance.

Contribution

The paper establishes the geometric convergence rate of Natural Policy Gradient and proposes adaptive step size methods for improved convergence.

Findings

Natural Policy Gradient converges linearly with geometric rate.

Adaptive step size variants further improve convergence speed.

Experimental results compare different policy gradient methods.

Abstract

Markov Decision Processes are classically solved using Value Iteration and Policy Iteration algorithms. Recent interest in Reinforcement Learning has motivated the study of methods inspired by optimization, such as gradient ascent. Among these, a popular algorithm is the Natural Policy Gradient, which is a mirror descent variant for MDPs. This algorithm forms the basis of several popular Reinforcement Learning algorithms such as Natural actor-critic, TRPO, PPO, etc, and so is being studied with growing interest. It has been shown that Natural Policy Gradient with constant step size converges with a sublinear rate of O(1/k) to the global optimal. In this paper, we present improved finite time convergence bounds, and show that this algorithm has geometric (also known as linear) asymptotic convergence rate. We further improve this convergence result by introducing a variant of Natural Policy Gradient with adaptive step sizes. Finally, we compare different variants of policy gradient methods experimentally.