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Self-supervised methods have become crucial for advancing deep learning byleveraging data itself to reduce the need for expensive annotations. However,the question of how to conduct self-supervised offline reinforcement learning(RL) in a principled way remains unclear. In this paper, we address this issueby investigating the theoretical benefits of utilizing reward-free data inlinear Markov Decision Processes (MDPs) within a semi-supervised setting.  Further, we propose a novel, Provable Data Sharing algorithm (PDS) to utilizesuch reward-free data for offline RL. PDS uses additional penalties on thereward function learned from labeled data to prevent overestimation, ensuring aconservative algorithm. Our results on various offline RL tasks demonstratethat PDS significantly improves the performance of offline RL algorithms withreward-free data. Overall, our work provides a promising approach to leveragingthe benefits of unlabeled data in offline RL while maintaining theoreticalguarantees. We believe our findings will contribute to developing more robustself-supervised RL methods.

The Provable Benefits of Unsupervised Data Sharing for Offline Reinforcement Learning