We study offline reinforcement learning (RL), which aims to learn an optimal policy based on a dataset collected a priori. Due to the lack of further interactions with the environment, offline RL suffers from the insufficient coverage of the dataset, which eludes most existing theoretical analysis. In this paper, we propose a pessimistic variant of the value iteration algorithm (PEVI), which incorporates an uncertainty quantifier as the penalty function. Such a penalty function simply flips the sign of the bonus function for promoting exploration in online RL, which makes it easily implementable and compatible with general function approximators. Without assuming the sufficient coverage of the dataset, we establish a data-dependent upper bound on the suboptimality of PEVI for general Markov decision processes (MDPs). When specialized to linear MDPs, it matches the information-theoretic lower bound up to multiplicative factors of the dimension and horizon. In other words, pessimism is not only provably efficient but also minimax optimal. In particular, given the dataset, the learned policy serves as the ``best effort'' among all policies, as no other policies can do better. Our theoretical analysis identifies the critical role of pessimism in eliminating a notion of spurious correlation, which emerges from the ``irrelevant'' trajectories that are less covered by the dataset and not informative for the optimal policy.

本文提出了一种悲观的价值迭代算法（PEVI），它通过引入一个不确定性量化器作为惩罚函数来解决离线强化学习中因数据集覆盖不足而导致的不足问题，并在泛化情况下对其次优性建立了数据相关的上限。

悲观策略在离线强化学习中能被证明是高效的吗？