Offline reinforcement learning suffers from the extrapolation error and value overestimation caused by out-of-distribution (OOD) actions. To mitigate this issue, value regularization approaches aim to penalize the learned value functions to assign lower values to OOD actions. However, existing value regularization methods lack a proper distinction between the regularization effects on in-distribution (ID) and OOD actions, and fail to guarantee optimal convergence results of the policy. To this end, we propose Supported Value Regularization (SVR), which penalizes the Q-values for all OOD actions while maintaining standard Bellman updates for ID ones. Specifically, we utilize the bias of importance sampling to compute the summation of Q-values over the entire OOD region, which serves as the penalty for policy evaluation.

As a learning policy may take actions beyond the knowledge of the behavior policy (referred to as Out-of-Distribution (OOD) actions), the Q-values of these OOD actions can be easily overestimated. Consequently, the learning policy becomes biasedly optimized using the incorrect recovered Q-value function. One commonly used idea to avoid the overestimation of Q-value is to make a pessimistic adjustment. Our key idea is to penalize the Q-values of OOD actions that correspond to high uncertainty. In this work, we propose Q-Distribution guided Q-learning (QDQ) which pessimistic Q-value on OOD regions based on uncertainty estimation. The uncertainty measure is based on the conditional Q-value distribution, which is learned via a high-fidelity and efficient consistency model. On the other hand, to avoid the overly conservative problem, we introduce an uncertainty-aware optimization objective to update 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 exhibits strong performance in the D4RL benchmark and shows significant improvements for many tasks.

Offline reinforcement learning (RL) defines the task of learning from a static logged dataset without continually interacting with the environment. The distribution shift between the learned policy and the behavior policy makes it necessary for the value function to stay conservative such that out-of-distribution (OOD) actions will not be severely overestimated. However, existing approaches, penalizing the unseen actions or regularizing with the behavior policy, are too pessimistic, which suppresses the generalization of the value function and hinders the performance improvement. This paper explores mild but enough conservatism for offline learning while not harming generalization. We propose Mildly Conservative Q-learning (MCQ), where OOD actions are actively trained by assigning them proper pseudo Q values. We theoretically show that MCQ induces a policy that behaves at least as well as the behavior policy and no erroneous overestimation will occur for OOD actions. Experimental results on the D4RL benchmarks demonstrate that MCQ achieves remarkable performance compared with prior work. Furthermore, MCQ shows superior generalization ability when transferring from offline to online, and significantly outperforms baselines. Our code is publicly available at https://github.com/dmksjfl/MCQ.