Functional Bilevel Optimization for Predictive Fairness

2026-07-06

AI Summary

This work addresses the challenge of enforcing fairness when sensitive attributes are continuous and high-dimensional—such as demographic score vectors or income profiles—where conventional fairness constraints become overly restrictive and difficult to optimize. The authors propose achieving mean demographic parity by minimizing the variance of the conditional prediction mean with respect to the sensitive attribute (DPVar), and for the first time formalize this objective as a functional bilevel optimization problem. To solve it, they introduce two novel algorithms: an exact hypergradient method based on a closed-form adjoint approach (FBO) and an implicit differentiation method via inner-loop unrolling (ITD), both applicable to squared loss and broader loss families. Evaluated on synthetic data and a new benchmark comprising 60 tabular regression tasks, the proposed methods significantly outperform strong baselines—including HSIC regularization, adversarial training, linear dependence removal, and generalized demographic parity—achieving the lowest or near-lowest regret on a combined fairness–accuracy metric.

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.

Problem

• predictive fairness
• bilevel optimization
• demographic parity
• fairness-accuracy trade-off
• sensitive attributes

Innovation

• Functional Bilevel Optimization
• Predictive Fairness
• DPVar
• Hypergradient
• Demographic Parity