What Hides behind Unfairness? Exploring Dynamics Fairness in Reinforcement Learning

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.