We study the \emph{offline reinforcement learning} (offline RL) problem, where the goal is to learn a rewardmaximizing policy in an unknown \emph{Markov Decision Process} (MDP) using the data coming from a policy $\mu$. In particular, we consider the sample complexity problems of offline RL for the finite horizon MDPs. Prior works derive the informationtheoretical lower bounds based on different datacoverage assumptions and their upper bounds are expressed by the covering coefficients which lack the explicit characterization of system quantities. In this work, we analyze the \emph{Adaptive Pessimistic Value Iteration} (APVI) algorithm and derive the suboptimality upper bound that nearly matches $ O\left(\sum_{h=1}^H\sum_{s_h,a_h}d^{\pi^\star}_h(s_h,a_h)\sqrt{\frac{\mathrm{Var}_{P_{s_h,a_h}}{(V^\star_{h+1}+r_h)}}{d^\mu_h(s_h,a_h)}}\sqrt{\frac{1}{n}}\right). $ We also prove an informationtheoretical lower bound to show this quantity is required under the weak assumption that $d^\mu_h(s_h,a_h)>0$ if $d^{\pi^\star}_h(s_h,a_h)>0$. Here $\pi^\star$ is a optimal policy, $\mu$ is the behavior policy and $d(s_h,a_h)$ is the marginal stateaction probability. We call this adaptive bound the \emph{intrinsic offline reinforcement learning bound} since it directly implies all the existing optimal results: minimax rate under uniform datacoverage assumption, horizonfree setting, single policy concentrability, and the tight problemdependent results. Later, we extend the result to the \emph{assumptionfree} regime (where we make no assumption on $ \mu$) and obtain the assumptionfree intrinsicmore »
Optimal Uniform OPE and Modelbased Offline Reinforcement Learning in TimeHomogeneous, RewardFree and TaskAgnostic Settings
This work studies the statistical limits of uniform convergence for offline policy evaluation (OPE) problems with modelbased methods (for episodic MDP) and provides a unified framework towards optimal learning for several wellmotivated offline tasks. Uniform OPE supΠQπ−Q̂ π<ϵ is a stronger measure than the pointwise OPE and ensures offline learning when Π contains all policies (the global class). In this paper, we establish an Ω(H2S/dmϵ2) lower bound (over modelbased family) for the global uniform OPE and our main result establishes an upper bound of Õ (H2/dmϵ2) for the \emph{local} uniform convergence that applies to all \emph{nearempirically optimal} policies for the MDPs with \emph{stationary} transition. Here dm is the minimal marginal stateaction probability. Critically, the highlight in achieving the optimal rate Õ (H2/dmϵ2) is our design of \emph{singleton absorbing MDP}, which is a new sharp analysis tool that works with the modelbased approach. We generalize such a modelbased framework to the new settings: offline taskagnostic and the offline rewardfree with optimal complexity Õ (H2log(K)/dmϵ2) (K is the number of tasks) and Õ (H2S/dmϵ2) respectively. These results provide a unified solution for simultaneously solving different offline RL problems.
 Publication Date:
 NSFPAR ID:
 10346205
 Journal Name:
 Advances in neural information processing systems
 Volume:
 34
 Page Range or eLocationID:
 1289012903
 ISSN:
 10495258
 Sponsoring Org:
 National Science Foundation
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