Learning trustworthy and reliable offline policies presents significant challenges due to the inherent uncertainty in pre-collected datasets. In this article, we propose a novel offline reinforcement learning (RL) method to tackle this issue. Inspired by the concepts of Lyapunov stability and control-invariant sets from control theory, the central idea is to introduce a restricted state space for the agent to operate within, which allows the learned models to exhibit reduced Bellman uncertainty and make reliable decisions. To achieve this, we regulate the expected Bellman uncertainty associated with the new policy, ensuring that its growth trend in subsequent states remains within acceptable limits. The resulting method, termed Lyapunov uncertainty control (LUC), is shown to guarantee that the agent remains within a low-uncertainty state enclosure throughout its entire trajectory. Furthermore, we perform extensive theoretical and experimental analysis to showcase the effectiveness and feasibility of the proposed LUC.
Jiang et al. (Wed,) studied this question.