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

• URL: http://arxiv.org/abs/2605.28233v1
• Date: Wed, 27 May 2026 09:45:16 GMT
• Title: Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings
• Abstract summary: principled methods for obtaining accurate predictions under relaxed fairness constraints are largely missing.<n>Our framework unifies both the emphaware and emphunaware settings and characterizes optimal prediction functions via optimal transport maps.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 \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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