Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings

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.

Machine Learning (stat.ML); Computers and Society (cs.CY); Machine Learning (cs.LG)

arXiv:2605.28233 [stat.ML]

(or arXiv:2605.28233v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2605.28233 Focus to learn more arXiv-issued DOI via DataCite

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