Title: Enforcing Group Fairness in Optimal Transport

Abstract: Achieving equity within matching algorithms is a critical hurdle in the distribution of limited resources and job opportunities. This study centers on Optimal Transport (OT) and defines a new standard for group fairness, stipulating that the likelihood of pairing individuals from distinct groups within an OT plan must align with a specified objective. To compute these perfectly fair transport plans efficiently, we initially introduce an adjusted Sinkhorn algorithm. However, because strict adherence to fairness can often compromise the overall quality of matches in real-world scenarios, we subsequently propose two methods for relaxation. The first approach addresses a penalized OT problem, for which we provide new finite-sample complexity bounds. The second method utilizes bilevel optimization to identify a ground cost function that yields a fair OT outcome, and we demonstrate a bound regarding fairness deviations when applied to unseen data. Lastly, we share experimental findings that highlight the efficacy of these techniques and the inherent balance between transport costs and fairness metrics.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC