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 »
NearOptimal Offline Reinforcement Learning via Double Variance Reduction
We consider the problem of offline reinforcement learning (RL)  a wellmotivated setting of RL that aims at policy optimization using only historical data. Despite its wide applicability, theoretical understandings of offline RL, such as its optimal sample complexity, remain largely open even in basic settings such as \emph{tabular} Markov Decision Processes (MDPs). In this paper, we propose OffPolicy Double Variance Reduction (OPDVR), a new variance reduction based algorithm for offline RL. Our main result shows that OPDVR provably identifies an ϵoptimal policy with O˜(H2/dmϵ2) episodes of offline data in the finitehorizon stationary transition setting, where H is the horizon length and dm is the minimal marginal stateaction distribution induced by the behavior policy. This improves over the best known upper bound by a factor of H. Moreover, we establish an informationtheoretic lower bound of Ω(H2/dmϵ2) which certifies that OPDVR is optimal up to logarithmic factors. Lastly, we show that OPDVR also achieves rateoptimal sample complexity under alternative settings such as the finitehorizon MDPs with nonstationary transitions and the infinite horizon MDPs with discounted rewards.
 Publication Date:
 NSFPAR ID:
 10346206
 Journal Name:
 Advances in neural information processing systems
 Volume:
 34
 Page Range or eLocationID:
 76777688
 ISSN:
 10495258
 Sponsoring Org:
 National Science Foundation
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