Q-Distribution guided Q-learning for offline reinforcement learning: Uncertainty penalized Q-value via consistency model

``Distribution shift'' is the main obstacle to the success of offline reinforcement learning. A learning policy may take actions beyond the behavior policy's knowledge, referred to as Out-of-Distribution (OOD) actions. The Q-values for these OOD actions can be easily overestimated. As a result, the learning policy is biased by using incorrect Q-value estimates. One common approach to avoid Q-value overestimation is to make a pessimistic adjustment. Our key idea is to penalize the Q-values of OOD actions associated with high uncertainty. In this work, we propose Q-Distribution Guided Q-Learning (QDQ), which applies a pessimistic adjustment to Q-values in OOD regions based on uncertainty estimation. This uncertainty measure relies on the conditional Q-value distribution, learned through a high-fidelity and efficient consistency model. Additionally, to prevent overly conservative estimates, we introduce an uncertainty-aware optimization objective for updating the Q-value function. The proposed QDQ demonstrates solid theoretical guarantees for the accuracy of Q-value distribution learning and uncertainty measurement, as well as the performance of the learning policy. QDQ consistently shows strong performance on the D4RL benchmark and achieves significant improvements across many tasks.