PAGE-PG: A Simple and Loopless Variance-Reduced Policy Gradient Method with Probabilistic Gradient Estimation

TL;DR

PAGE-PG introduces a novel loopless variance-reduced policy gradient method using probabilistic gradient estimation, achieving optimal sample complexity and demonstrating competitive performance on control tasks.

Contribution

It proposes PAGE-PG, a new loopless variance-reduced policy gradient algorithm that uses probabilistic switching and importance sampling for unbiased gradient estimation.

Findings

Achieves $ ilde{O}(rac{1}{ ext{epsilon}^3})$ sample complexity for $ ext{epsilon}$-stationary solutions.

Matches the sample complexity of leading methods under similar conditions.

Shows competitive numerical performance on classical control tasks.

Abstract

Despite their success, policy gradient methods suffer from high variance of the gradient estimate, which can result in unsatisfactory sample complexity. Recently, numerous variance-reduced extensions of policy gradient methods with provably better sample complexity and competitive numerical performance have been proposed. After a compact survey on some of the main variance-reduced REINFORCE-type methods, we propose ProbAbilistic Gradient Estimation for Policy Gradient (PAGE-PG), a novel loopless variance-reduced policy gradient method based on a probabilistic switch between two types of updates. Our method is inspired by the PAGE estimator for supervised learning and leverages importance sampling to obtain an unbiased gradient estimator. We show that PAGE-PG enjoys a $\mathcal{O}\left( \epsilon^{-3} \right)$ average sample complexity to reach an $\epsilon$-stationary solution, which matches the sample complexity of its most competitive counterparts under the same setting. A numerical evaluation confirms the competitive performance of our method on classical control tasks.