arXiv Machine Learning October 9, 2026 By Ieva Petrulionyte, Julien Mairal, Michael Arbel

Directly Optimizing Mean Demographic Parity for Nonlinear Regression

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The paper introduces DPVar, a fairness metric that measures the variance of the conditional mean prediction to directly optimize mean demographic parity in nonlinear regression. It presents two solvers—FBO, using a closed‑form hypergradient, and ITD, which differentiates through the conditional‑mean estimator updates—to handle the resulting functional bilevel problem. Experiments on 21 tabular datasets and the Communities & Crime data show that these methods achieve competitive or superior accuracy‑fairness trade‑offs compared to existing approaches.

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