Can Safety Transfer Across Embodiments? Corrective Supervision for Offline Safe Reinforcement Learning

Offline safe reinforcement learning relies on safety-relevant experience from a fixed dataset, which may be limited for a particular embodiment. Other embodiments may have demonstrated useful corrective behavior, but differences in actions and dynamics make this experience difficult to reuse. Can their observed motion provide safety supervision beyond what the target can learn from its own data? We investigate this question through cross-embodiment corrective supervision (CECS), an offline approach that transfers observed source motion into target-native training signals. The method retrieves safety-relevant source motions in locally matched task contexts, translates them into target-native actions via target inverse dynamics, filters the resulting corrections with target-side safety information, and uses them to refine the target policy. This formulation transfers corrective behavior rather than directly sharing actions or policies across embodiments. Experiments across different morphologies and task families show improved safety over pretrained target policies and competitive safety–reward trade-offs against offline safe RL baselines. Controlled comparisons at shared contexts and equal correction counts show that source supervision improves safety beyond equally trained target-only retrieval. Shuffling the corrective labels substantially degrades performance, highlighting the importance of matching corrections to the context. A matched-state analysis further shows that the refined policy reduces accumulated cost through sustained control while retaining most task progress. These results demonstrate the value of cross-embodiment motion as corrective supervision and identify context matching as an important factor in its effective use.