Title: Uncertainty-based Multi-Task Data Sharing for Offline Reinforcement Learning. Abstract: Offline Reinforcement Learning (RL) has shown promising results in learning a task-specific policy from a fixed dataset. However, successful offline RL often relies heavily on the coverage and quality of the given dataset. In scenarios where the dataset for a specific task is limited, a natural approach is to improve offline RL with datasets from other tasks, namely, to conduct Multi-Task Data Sharing (MTDS). Nevertheless, directly sharing datasets from other tasks exacerbates the distribution shift in offline RL. As a remedy, previous attempts share only partial data that maximizes a conservative value function. However, such attempts are inefficient in calculating the policy constraints and abandon a large portion of datasets, which could be potentially informative. In this paper, we propose an uncertainty-based MTDS approach that shares the entire dataset without data selection. We further provide theoretical analysis, which shows that the optimality gap of our method is only related to the expected data coverage of the shared dataset, thus resolving the distribution shift issue in data sharing. Empirically, we construct an MTDS benchmark and collect datasets from three challenging domains. The experimental results show our algorithm outperforms the previous state-of-the-art methods in challenging MTDS problems.