From Fragile to Certified: Wasserstein Audits of Group Fairness Under Distribution Shift

Group-fairness metrics (e.g., equalized odds) can vary sharply across resamples and are especially brittle under distribution shift, undermining reliable audits. We propose a Wasserstein distributionally robust framework that certifies worst-case group fairness over a ball of plausible test distributions centered at the empirical law. Our formulation unifies common group fairness notions via a generic conditional-probability functional and defines ε-Wasserstein Distributional Fairness (ε-WDF) as the audit target. Leveraging strong duality, we derive tractable reformulations and an efficient estimator (DRUNE) for ε-WDF. We prove feasibility and consistency and establish finite-sample certification guarantees for auditing fairness, along with quantitative bounds under smoothness and margin conditions. Across standard benchmarks and classifiers, ε-WDF delivers stable fairness assessments under distribution shift, providing a principled basis for auditing and certifying group fairness beyond observational data.