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

NeurIPS 2026 · Learning theory and algorithms › Fairness · approach: Minimax fairness via sampling · 0 citations (OpenAlex)

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Formulates relaxed demographic-parity regression as a penalized optimal transport problem, derives closed-form pointwise OT maps for W2^2 and TV penalties in aware and unaware settings, and proposes a discrete-OT post-processing algorithm that matches or beats FairReg on Law School and Communities and Crime.

Problem

Fairness-accuracy trade-off for regression under relaxed demographic parity when the sensitive attribute is unavailable at inference (unaware setting); existing relaxed unaware methods rely on grid discretization and stochastic optimization.

Approach

Reduces the penalized fair regression problem (aware and unaware, W2^2 and TV penalties) to an OT problem between two 2D measures over (eta, Delta), yielding pointwise closed-form transport maps and a deterministic discrete-OT post-processing estimator.

Key results

• On Law School and Communities and Crime, OT-U W2 achieves better accuracy-fairness trade-offs than FairReg on the continuous W2 metric and is competitive on KS and TV.
• W2-penalized models achieve better trade-offs than TV-penalized ones even when evaluated on TV.
• The discrete OT step runs in seconds for n around 10^4, significantly faster than FairReg's stochastic gradient approach.

Surprising findings

• W2-penalized models achieve better trade-offs than TV-penalized ones even when evaluated on the TV metric.

Limitations

• Restricted to TV and W2^2 penalties (not general OT_c costs).
• Restricted to binary sensitive attributes; multi-group extension unresolved.
• Post-processing performance depends on quality of estimators for eta and Delta; no statistical guarantees given.

Experimental setup

Datasets: Law School Admissions Communities and Crime

Benchmarks: Law School Admissions Communities and Crime

Metrics: MSE W2 unfairness TV unfairness KS distance on 50-bin grid

Baselines: FairReg ERM OT-A W2 OT-A TV OT plug-in S-hat W2

Builds on: FairReg Wasserstein barycenter fair regression Gaskin/Chzhen-style OT fair regression (OT-A) POT library

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