Wasserstein Robust Classification with Fairness Constraints

TL;DR

This paper introduces a Wasserstein distributionally robust classification model that incorporates fairness constraints to improve fairness in predictions while maintaining accuracy, suitable for large-scale problems.

Contribution

It develops a novel Wasserstein-based robust classification framework with fairness constraints, including scalable convex reformulations and extensions for label and sensitive attribute uncertainties.

Findings

Improves fairness with negligible accuracy loss.

Provides scalable convex reformulations for large problems.

Demonstrates robustness against distributional uncertainties.

Abstract

We propose a distributionally robust classification model with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-$\infty$ Wasserstein ambiguity set centered at the empirical distribution to model distributional uncertainty and derive a conservative reformulation for the worst-case equal opportunity unfairness measure. We establish that the model is equivalent to a mixed binary optimization problem, which can be solved by standard off-the-shelf solvers. To improve scalability, we further propose a convex, hinge-loss-based model for large problem instances whose reformulation does not incur any binary variables. Moreover, we also consider the distributionally robust learning problem with a generic ground transportation cost to hedge against the uncertainties in the label and sensitive attribute. Finally, we numerically demonstrate that our proposed approaches improve fairness with negligible loss of predictive accuracy.