Functional Bilevel Optimization for Predictive Fairness
This work provides a principled and effective optimization framework for predictive fairness in complex, high-dimensional sensitive attribute settings, addressing a key limitation of existing indirect or adversarial methods.
The paper tackles the problem of enforcing fairness in machine learning when sensitive attributes are continuous and high-dimensional, proposing a functional bilevel optimization approach that directly optimizes mean demographic parity via DPVar. Their methods achieve the lowest or near-lowest fairness-accuracy regret on synthetic and semi-synthetic benchmarks, outperforming existing baselines.
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.