Bellman-consistent Pessimism for Offline Reinforcement Learning

Tengyang Xie, Ching-An Cheng, Nan Jiang, Paul Mineiro, Alekh Agarwal

Keywords: offline reinforcement learning, Bellman-consistent pessimism, sample complexity bounds, linear MDP, function approximation

TL;DR: We introduce the notion of Bellman-consistent pessimism for general function approximation in offline reinforcement learning.

Abstract: 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 function approximation where stronger expressivity 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.

Code Of Conduct: I certify that all co-authors of this work have read and commit to adhering to the NeurIPS Statement on Ethics, Fairness, Inclusivity, and Code of Conduct.