PC-PG: Policy Cover Directed Exploration for Provable Policy Gradient Learning

TL;DR

This paper introduces PC-PG, a policy gradient algorithm that balances exploration and exploitation using a policy cover, with provable guarantees and empirical validation in various reinforcement learning settings.

Contribution

The paper proposes PC-PG, a novel policy gradient method with ensemble-based exploration, offering theoretical guarantees under model misspecification and empirical validation.

Findings

Polynomial sample complexity for tabular and linear MDPs

Strong guarantees under model misspecification

Effective exploration in reward-free and reward-driven tasks

Abstract

Direct policy gradient methods for reinforcement learning are a successful approach for a variety of reasons: they are model free, they directly optimize the performance metric of interest, and they allow for richly parameterized policies. Their primary drawback is that, by being local in nature, they fail to adequately explore the environment. In contrast, while model-based approaches and Q-learning directly handle exploration through the use of optimism, their ability to handle model misspecification and function approximation is far less evident. This work introduces the the Policy Cover-Policy Gradient (PC-PG) algorithm, which provably balances the exploration vs. exploitation tradeoff using an ensemble of learned policies (the policy cover). PC-PG enjoys polynomial sample complexity and run time for both tabular MDPs and, more generally, linear MDPs in an infinite dimensional RKHS. Furthermore, PC-PG also has strong guarantees under model misspecification that go beyond the standard worst case $\ell_{\infty}$ assumptions; this includes approximation guarantees for state aggregation under an average case error assumption, along with guarantees under a more general assumption where the approximation error under distribution shift is controlled. We complement the theory with empirical evaluation across a variety of domains in both reward-free and reward-driven settings.