提出公平匹配新方法，确保不同群体间匹配比例符合预设目标。
Optimal Transport under Group Fairness Constraints
- 用改进的Sinkhorn算法实现完全公平的运输计划
- 在保证公平的前提下，匹配质量下降可控，且有理论保证
- 适合资源分配、招聘等需兼顾公平与效率的场景
在资源与职位分配中，确保匹配算法的公平性是一个关键挑战。针对最优传输（Optimal Transport, OT），本文提出一种新的群体公平性概念：任意两个群体间的个体匹配概率需满足预设目标。首先，我们设计了一种改进的Sinkhorn算法，可高效计算完全公平的传输方案。由于严格公平可能显著降低实际匹配质量，我们进一步提出两种松弛策略：第一种是求解带惩罚项的OT问题，并给出新的有限样本复杂度保证；第二种采用双层优化学习一个能诱导公平结果的基代价函数，并建立对未见数据匹配公平性偏差的上界。最后，我们通过实验验证了所提方法的有效性，展示了公平性与传输成本之间的权衡关系。
原文摘要 · Abstract (English)
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.
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