公平回归的几何：统一 aware 与 unaware 场景的松弛公平回归框架

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Abstract: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 aware and 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 parity for a subset of individuals. Building on these theoretical characterizations, we propose FAUST, an algorithm that is simple to implement, computationally efficient, and consistently matches or outperforms state-of-the-art baselines on real-world benchmarks.

Subjects:	Machine Learning (stat.ML); Computers and Society (cs.CY); Machine Learning (cs.LG)
Report number:	hal-05625006
Cite as:	arXiv:2605.28233 [stat.ML]
	(or arXiv:2605.28233v2 [stat.ML] for this version)
	https://doi.org/10.48550/arXiv.2605.28233 arXiv-issued DOI via DataCite

Submission history

From: Marie Generali Lince [view email]
[v1] Wed, 27 May 2026 09:45:16 UTC (1,725 KB)
[v2] Fri, 30 Oct 2026 12:27:00 UTC (831 KB)