Fairness-accuracy trade-offs are a central concern in the deployment of fairness-aware machine learning methods. When sensitive attributes are unavailable at inference time-the so called unawareness setting, principled methods for obtaining accurate predictions under relaxed fairness constraints are largely missing. In this work, we address this gap by formulating regression under a demographic parity penalty as an optimal transport problem. Our framework unifies both the \emph{aware} and \emph{unaware} settings and characterizes optimal prediction functions via optimal transport maps, under both squared Wasserstein-2 and Total Variation penalties. These results reveal that the choice of penalty reflects fundamentally different fairness philosophies: the Wasserstein penalty induces a smooth, population-wide compromise, while Total Variation enforces exact parity for a subset of individuals. Building on these theoretical characterizations, we propose an algorithm that is simple to implement, computationally efficient, and consistently matches or outperforms state-of-the-art baselines on real-world benchmarks.

翻译：公平性与准确性之间的权衡是部署公平感知机器学习方法时的核心关注点。当敏感属性在推理时不可用时——即所谓的不知情设置，目前缺乏在松弛公平约束下获取精确预测的严谨方法。本研究通过将人口统计均等惩罚下的回归问题表述为最优传输问题，填补了这一空白。我们的框架统一了知情与不知情两种设置，并利用最优传输映射刻画了平方Wasserstein-2惩罚与全变差惩罚下的最优预测函数。这些结果揭示出惩罚选择反映本质不同的公平性哲学：Wasserstein惩罚诱导出平滑的人口范围妥协，而全变差惩罚则为个体子集强制执行精确均等。基于这些理论刻画，我们提出一种实现简单、计算高效且在真实世界基准测试中持续达到或超越当前最优基线的算法。