The use of pessimism, when reasoning about datasets lacking exhaustive exploration has recently gained prominence in offline reinforcement learning. Despite the robustness it adds to the algorithm, overly pessimistic reasoning can be equally damaging in precluding the discovery of good policies, which is an issue for the popular bonus-based pessimism. In this paper, we introduce the notion of Bellman-consistent pessimism for general function approximation: instead of calculating a point-wise lower bound for the value function, we implement pessimism at the initial state over the set of functions consistent with the Bellman equations. Our theoretical guarantees only require Bellman closedness as standard in the exploratory setting, in which case bonus-based pessimism fails to provide guarantees. Even in the special case of linear MDPs where stronger function-approximation assumptions hold, our result improves upon a recent bonus-based approach by $\mathcal{O}(d)$ in its sample complexity when the action space is finite. Remarkably, our algorithms automatically adapt to the best bias-variance tradeoff in the hindsight, whereas most prior approaches require tuning extra hyperparameters a priori.

本文介绍了一种Bellman-consistent的悲观算法，在深度学习的数据集中使用较为普遍，通过对探索性场景的标准Bellman闭合性理论保证了算法的鲁棒性，并且在样本复杂度上比其他算法有显著提高。

离线强化学习的Bellman一致悲观算法