Robustness Within a Fairness Budget: Parity Frontiers and Equal-Opportunity Reversal

Pablo Rivas, Jeremy Frank

Adversarial training protects predictive performance under attack but does not determine how decisions are distributed across protected groups. We formulate binary classification as projected gradient descent (PGD) adversarial-risk minimization under a squared soft demographic-parity (DP) budget, optimized with projected multiplier and one-sided penalty updates. On Adult Income, using the binary sex field supplied by the benchmark for group auditing but excluding it from prediction, we test logistic regression and a one-hidden-layer multilayer perceptron (MLP) across three paired seeds, four PGD strengths, and five budgets. At $\varepsilon=0.3$, PGD training improves balanced accuracy over empirical-risk minimization (ERM) by $7.77$ and $11.45$ percentage points and removes $85.7\%$ and $89.5\%$ of attack-induced growth in hard demographic-parity difference (DPD). At the representative interior value $τ=0.015$, constrained training cuts DPD relative to PGD training by $52.2\%$ and $49.2\%$, while remaining $3.18$ and $8.34$ balanced-accuracy points above ERM. Across all eight seed-averaged model-attack paths, the sampled budget path strictly orders DPD and accuracy and reverses…