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.
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BibTeX
@misc{lince2026geometry,
title = {{Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings}},
author = {Marie Generali Lince and Vincent Divol and Rémi Flamary and Solenne Gaucher and Patrick Loiseau},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.28233},
eprint = {2605.28233},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.28233},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings
AU - Marie Generali Lince
AU - Vincent Divol
AU - Rémi Flamary
AU - Solenne Gaucher
AU - Patrick Loiseau
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2605.28233
UR - https://arxiv.org/abs/2605.28233
AB - 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.
ER -