统一公平回归的有知与无知场景，提出高效算法实现宽松公平约束下的精准预测。
Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings
- 将公平回归建模为最优传输问题，统一处理有知与无知两种场景。
- 在真实数据集上，新算法性能优于或持平现有先进方法。
- 揭示不同惩罚项对应不同公平理念，提供理论指导选择策略。
公平性与准确性的权衡是部署公平感知机器学习方法的核心挑战。当敏感属性在推理阶段不可用（即‘无知’设置）时，满足宽松公平约束的精确预测方法仍缺乏系统性方案。本文将受人口均等性惩罚的回归问题形式化为最优传输问题，统一了‘有知’与‘无知’设置，并通过最优传输映射刻画最优预测函数，适用于平方Wasserstein-2和总变差惩罚。结果表明，惩罚项的选择反映根本不同的公平哲学：Wasserstein惩罚带来全局平滑妥协，而总变差惩罚对部分个体强制实现精确均等。基于此理论，我们提出一种简单易实现、计算高效的算法，在真实世界基准测试中持续优于或匹配现有最先进方法。
原文摘要 · Abstract (English)
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.
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