Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings
This work provides a theoretically grounded framework for fair regression in the unaware setting, which is a practical bottleneck for deploying fairness-aware models.
The paper addresses the lack of principled methods for fair regression under demographic parity when sensitive attributes are unavailable at inference time. It formulates the problem as optimal transport, unifying aware and unaware settings, and proposes an algorithm that matches or outperforms state-of-the-art baselines on real-world benchmarks.
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.