Functional Bilevel Optimization for Predictive Fairness
2026-07-06 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address fairness in machine learning when sensitive attributes are complex, like detailed demographic scores, making usual independence rules too strict. They focus on mean demographic parity using a measure called DPVar, turning the problem into a special two-level optimization task. They introduce two algorithms, FBO and ITD, that handle this task efficiently and work well with different loss types. Testing on synthetic and real datasets shows their methods perform better or as well as existing fairness approaches, balancing accuracy and fairness effectively.
mean demographic parityDPVarbilevel optimizationfairness-accuracy trade-offsensitive attributesadjoint methodhypergradientHSICadversarial trainingtabular regression datasets
Authors
Ieva Petrulionyte, Julien Mairal, Michael Arbel
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.