Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914607421980672 |
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| author | Lince, M. Generali Divol, V. Flamary, R. Gaucher, S. Loiseau, P. |
| author_facet | Lince, M. Generali Divol, V. Flamary, R. Gaucher, S. Loiseau, P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28233 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings Lince, M. Generali Divol, V. Flamary, R. Gaucher, S. Loiseau, P. Machine Learning Computers and Society 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. |
| title | Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings |
| topic | Machine Learning Computers and Society |
| url | https://arxiv.org/abs/2605.28233 |