Optimal Transport under Group Fairness Constraints

2026-01-12

AI Summary

This work addresses the challenge of group fairness in optimal transport for resource allocation by proposing a novel fair optimal transport framework. It introduces, for the first time, fairness constraints based on group-wise matching probabilities and develops the FairSinkhorn algorithm to achieve exact fair matching. Furthermore, the framework learns a fairness-inducing cost function through a convex penalty term within a bilevel optimization scheme. Theoretically, the study establishes finite-sample complexity bounds for optimal transport under fairness constraints. Experimental results demonstrate that the proposed method effectively balances matching quality with fairness guarantees and exhibits strong generalization performance on unseen data.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two individuals from any two given groups in the OT plan satisfies a predefined target. We first propose a modified Sinkhorn algorithm to compute perfectly fair transport plans efficiently. Since exact fairness can significantly degrade matching quality in practice, we then develop two relaxation strategies. The first one involves solving a penalized OT problem, for which we derive novel finite-sample complexity guarantees. Our second strategy leverages bilevel optimization to learn a ground cost that induces a fair OT solution, and we establish a bound on the deviation of fairness when matching unseen data. Finally, we present empirical results illustrating the performance of our approaches and the trade-off between fairness and transport cost.

Problem

• Optimal Transport
• Group Fairness
• Matching Algorithms
• Fairness Constraints
• Resource Allocation

Innovation

• Optimal Transport
• Group Fairness
• FairSinkhorn
• Bilevel Optimization
• Penalized OT