Directly Optimizing Mean Demographic Parity for Nonlinear Regression

We focus on regression settings where the fairness goal is to equalize average predictions across values of a sensitive attribute, a criterion known as mean demographic parity. Directly optimizing this criterion is difficult because it depends on a conditional mean that is unknown and changes during training. Common dependence penalties and adversarial methods do not estimate this conditional mean; instead, they push predictions toward full independence. This stronger constraint can reduce accuracy even when average predictions are already equal. Existing conditional-mean methods are limited to linear predictors or low-dimensional sensitive attributes. We enable direct optimization of mean demographic parity using DPVar, a fairness measure defined as the variance of the conditional mean prediction. Because the conditional mean must be estimated as the predictor changes, optimizing DPVar leads to a functional bilevel problem. We develop two solvers: FBO, which uses a closed-form hypergradient, and an iterative-differentiation (ITD) solver that differentiates through updates of the conditional-mean estimator. Unlike previous conditional-mean methods, our approach applies to nonlinear predictors and high-dimensional continuous sensitive attributes. Across a semi-synthetic benchmark built from 21 tabular regression datasets and Communities & Crime data, FBO and ITD recover competitive or better accuracy-DPVar trade-offs than existing methods.