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The problem of Offline Policy Evaluation (OPE) in Reinforcement Learning (RL)is a critical step towards applying RL in real-life applications. Existing workon OPE mostly focus on evaluating a fixed target policy $\pi$, which does notprovide useful bounds for offline policy learning as $\pi$ will then bedata-dependent. We address this problem by simultaneously evaluating allpolicies in a policy class $\Pi$ -- uniform convergence in OPE -- and obtainnearly optimal error bounds for a number of global / local policy classes. Ourresults imply that the model-based planning achieves an optimal episodecomplexity of $\widetilde{O}(H^3/d_m\epsilon^2)$ in identifying an$\epsilon$-optimal policy under the time-inhomogeneous episodic MDP model ($H$is the planning horizon, $d_m$ is a quantity that reflects the exploration ofthe logging policy $\mu$). To the best of our knowledge, this is the first timethe optimal rate is shown to be possible for the offline RL setting and thepaper is the first that systematically investigates the uniform convergence inOPE.

Near-Optimal Provable Uniform Convergence in Offline Policy Evaluation for Reinforcement Learning