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

Decisions made by machine learning models may have lasting impacts over time, making long-term fairness a crucial consideration. It has been shown that when ignoring the long-term effect, naively imposing fairness criterion in static settings can actually exacerbate bias over time. To explicitly address biases in sequential decision-making, recent works formulate long-term fairness notions in Markov Decision Process (MDP) framework. They define the long-term bias to be the sum of static bias over each time step. However, we demonstrate that naively summing up the step-wise bias can cause a false sense of fairness since it fails to consider the importance difference of different time steps during transition. In this work, we introduce a long-term fairness notion called Equal Long-term Benefit Rate (ELBERT), which explicitly considers varying temporal importance and adapts static fairness principles to the sequential setting. Moreover, we show that the policy gradient of Long-term Benefit Rate can be analytically reduced to standard policy gradient. This makes standard policy optimization methods applicable for reducing the bias, leading to our proposed bias mitigation method ELBERT-PO. Experiments on three sequential decision making environments show that ELBERT-PO significantly reduces bias and maintains high utility. Code is available at https://github.com/Yuancheng-Xu/ELBERT.