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  1. Algorithmic decisions made by machine learning models in high-stakes domains may have lasting impacts over time. However, naive applications of standard fairness criterion in static settings over temporal domains may lead to delayed and adverse effects. To understand the dynamics of performance disparity, we study a fairness problem in Markov decision processes (MDPs). Specifically, we propose return parity, a fairness notion that requires MDPs from different demographic groups that share the same state and action spaces to achieve approximately the same expected time-discounted rewards. We first provide a decomposition theorem for return disparity, which decomposes the return disparity of any two MDPs sharing the same state and action spaces into the distance between group-wise reward functions, the discrepancy of group policies, and the discrepancy between state visitation distributions induced by the group policies. Motivated by our decomposition theorem, we propose algorithms to mitigate return disparity via learning a shared group policy with state visitation distributional alignment using integral probability metrics. We conduct experiments to corroborate our results, showing that the proposed algorithm can successfully close the disparity gap while maintaining the performance of policies on two real-world recommender system benchmark datasets. 
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