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

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