  Decisions made by machine learning models can have lasting impacts, making
long-term fairness a critical consideration. It has been observed that ignoring
the long-term effect and directly applying fairness criterion in static
settings can actually worsen bias over time. To address biases in sequential
decision-making, we introduce a long-term fairness concept named Equal
Long-term Benefit Rate (ELBERT). This concept is seamlessly integrated into a
Markov Decision Process (MDP) to consider the future effects of actions on
long-term fairness, thus providing a unified framework for fair sequential
decision-making problems. ELBERT effectively addresses the temporal
discrimination issues found in previous long-term fairness notions.
Additionally, we demonstrate that the policy gradient of Long-term Benefit Rate
can be analytically simplified to standard policy gradients. This
simplification makes conventional policy optimization methods viable for
reducing bias, leading to our bias mitigation approach ELBERT-PO. Extensive
experiments across various diverse sequential decision-making environments
consistently reveal that ELBERT-PO significantly diminishes bias while
maintaining high utility. Code is available at
https://github.com/umd-huang-lab/ELBERT.
