A Hybrid Stochastic Policy Gradient Algorithm for Reinforcement Learning

TL;DR

This paper introduces a new hybrid stochastic policy gradient estimator and an associated algorithm that improves convergence rates for constrained reinforcement learning problems, demonstrating superior performance over existing methods.

Contribution

It develops a novel hybrid estimator combining unbiased and biased gradient estimators, and proposes a Proximal Hybrid Stochastic Policy Gradient Algorithm with improved convergence guarantees.

Findings

Achieves the best-known trajectory complexity of O(ε^{-3}) for the composite problem.

Outperforms existing methods like REINFORCE and SVRPG in numerical experiments.

Shows advantages of composite settings over non-composite ones in certain RL problems.

Abstract

We propose a novel hybrid stochastic policy gradient estimator by combining an unbiased policy gradient estimator, the REINFORCE estimator, with another biased one, an adapted SARAH estimator for policy optimization. The hybrid policy gradient estimator is shown to be biased, but has variance reduced property. Using this estimator, we develop a new Proximal Hybrid Stochastic Policy Gradient Algorithm (ProxHSPGA) to solve a composite policy optimization problem that allows us to handle constraints or regularizers on the policy parameters. We first propose a single-looped algorithm then introduce a more practical restarting variant. We prove that both algorithms can achieve the best-known trajectory complexity $\mathcal{O}\left(\varepsilon^{-3}\right)$ to attain a first-order stationary point for the composite problem which is better than existing REINFORCE/GPOMDP $\mathcal{O}\left(\varepsilon^{-4}\right)$ and SVRPG $\mathcal{O}\left(\varepsilon^{-10/3}\right)$ in the non-composite setting. We evaluate the performance of our algorithm on several well-known examples in reinforcement learning. Numerical results show that our algorithm outperforms two existing methods on these examples. Moreover, the composite settings indeed have some advantages compared to the non-composite ones on certain problems.