In sequential decision-making problems involving sensitive attributes like race and gender, reinforcement learning (RL) agents must carefully consider long-term fairness while maximizing returns. Recent works have proposed many different types of fairness notions, but how unfairness arises in RL problems remains unclear. In this paper, we address this gap in the literature by investigating the sources of inequality through a causal lens. We first analyse the causal relationships governing the data generation process and decompose the effect of sensitive attributes on long-term well-being into distinct components. We then introduce a novel notion called dynamics fairness, which explicitly captures the inequality stemming from environmental dynamics, distinguishing it from those induced by decision-making or inherited from the past. This notion requires evaluating the expected changes in the next state and the reward induced by changing the value of the sensitive attribute while holding everything else constant. To quantitatively evaluate this counterfactual concept, we derive identification formulas that allow us to obtain reliable estimations from data. Extensive experiments demonstrate the effectiveness of the proposed techniques in explaining, detecting, and reducing inequality in reinforcement learning. We publicly release code at https://github.com/familyld/InsightFair.

Machine learning (ML) has demonstrated remarkable capabilities across many real-world systems, from predictive modeling to intelligent automation. However, the widespread integration of machine learning also makes it necessary to ensure machine learning-driven decision-making systems do not violate ethical principles and values of society in which they operate. As ML-driven decisions proliferate, particularly in cases involving sensitive attributes such as gender, race, and age, to name a few, the need for equity and impartiality has emerged as a fundamental concern. In situations demanding real-time decision-making, fairness objectives become more nuanced and complex: instantaneous fairness to ensure equity in every time slot, and long-term fairness to ensure fairness over a period of time. There is a growing awareness that real-world systems that operate over long periods and require fairness over different timelines. However, existing approaches mainly address dynamic costs with time-invariant fairness constraints, often disregarding the challenges posed by time-varying fairness constraints. To bridge this gap, this work introduces a framework for ensuring long-term fairness within dynamic decision-making systems characterized by time-varying fairness constraints. We formulate the decision problem with fairness constraints over a period as a constrained online optimization problem. A novel online algorithm, named LoTFair, is presented that solves the problem 'on the fly'. We prove that LoTFair can make overall fairness violations negligible while maintaining the performance over the long run.