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Nearly Horizon-Free Offline Reinforcement Learning
Tongzheng Ren · Jialian Li · Bo Dai · Simon Du · Sujay Sanghavi

Tue Dec 07 04:30 PM -- 06:00 PM (PST) @ None #None
We revisit offline reinforcement learning on episodic time-homogeneous Markov Decision Processes (MDP). For tabular MDP with $S$ states and $A$ actions, or linear MDP with anchor points and feature dimension $d$, given the collected $K$ episodes data with minimum visiting probability of (anchor) state-action pairs $d_m$, we obtain nearly horizon $H$-free sample complexity bounds for offline reinforcement learning when the total reward is upper bounded by 1. Specifically:• For offline policy evaluation, we obtain an $\tilde{O}\left(\sqrt{\frac{1}{Kd_m}} \right)$ error bound for the plug-in estimator, which matches the lower bound up to logarithmic factors and does not have additional dependency on $\mathrm{poly}(H, S, A, d)$ in higher-order term.• For offline policy optimization, we obtain an $\tilde{O}\left(\sqrt{\frac{1}{Kd_m}} + \frac{\min(S, d)}{Kd_m}\right)$ sub-optimality gap for the empirical optimal policy, which approaches the lower bound up to logarithmic factors and a high-order term, improving upon the best known result by [Cui and Yang 2020] that has additional $\mathrm{poly} (H, S, d)$ factors in the main term.To the best of our knowledge, these are the first set of nearly horizon-free bounds for episodic time-homogeneous offline tabular MDP and linear MDP with anchor points. Central to our analysis is a simple yet effective recursion based method to bound a "total variance" term in the offline scenarios, which could be of individual interest.

Author Information

Tongzheng Ren (UT Austin)
Jialian Li (Tsinghua University)
Bo Dai (Google Brain)
Simon Du (University of Washington)
Sujay Sanghavi (UT-Austin)

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