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Decisions made by machine learning models may have lasting impacts over time,making long-term fairness a crucial consideration. It has been shown that whenignoring the long-term effect, naively imposing fairness criterion in staticsettings can actually exacerbate bias over time. To explicitly address biasesin sequential decision-making, recent works formulate long-term fairnessnotions in Markov Decision Process (MDP) framework. They define the long-termbias to be the sum of static bias over each time step. However, we demonstratethat naively summing up the step-wise bias can cause a false sense of fairnesssince it fails to consider the importance difference of different time stepsduring transition. In this work, we introduce a long-term fairness notioncalled Equal Long-term Benefit Rate (ELBERT), which explicitly considersvarying temporal importance and adapts static fairness principles to thesequential setting. Moreover, we show that the policy gradient of Long-termBenefit Rate can be analytically reduced to standard policy gradient. Thismakes standard policy optimization methods applicable for reducing the bias,leading to our proposed bias mitigation method ELBERT-PO. Experiments on threesequential decision making environments show that ELBERT-PO significantlyreduces bias and maintains high utility. Code is available athttps://github.com/Yuancheng-Xu/ELBERT.

Equal Long-term Benefit Rate: Adapting Static Fairness Notions to Sequential Decision Making