Functional Bilevel Optimization for Predictive Fairness

• URL: http://arxiv.org/abs/2607.05098v1
• Date: Mon, 06 Jul 2026 13:56:16 GMT
• Title: Functional Bilevel Optimization for Predictive Fairness
• Abstract summary: We consider mean demographic parity through DPVar, the variance of the conditional-mean prediction given the sensitive attribute, and show that optimizing it yields a functional bilevel problem.<n>We propose two algorithms for this problem: FBO, which uses a closed-form adjoint we derive for the squared-loss case to obtain an exact hypergradient, and ITD, which differentiates through unrolled inner steps and extends beyond squared loss.
• Score: 25.649081304879218
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: When sensitive attributes are continuous and high-dimensional $-$ demographic score vectors, posteriors over attributes, age or income profiles $-$ enforcing full statistical independence is often too restrictive, and existing relaxations rely on indirect dependence penalties or adversarial schemes that do not directly target the fairness-accuracy trade-off. We instead consider mean demographic parity through DPVar, the variance of the conditional-mean prediction given the sensitive attribute, and show that optimizing it yields a functional bilevel problem. We propose two algorithms for this problem: FBO, which uses a closed-form adjoint we derive for the squared-loss case to obtain an exact hypergradient, and ITD, which differentiates through unrolled inner steps and extends beyond squared loss. On synthetic data and a new semi-synthetic benchmark built from 60 tabular regression datasets, both methods achieve the lowest or near-lowest aggregate fairness-accuracy regret, and consistently match or outperform strong HSIC, adversarial, linear-dependence, and generalized-DP baselines.

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