Too Relaxed to Be Fair

We address the problem of classification under fairness constraints. Given a notion of fairness, the goal is to learn a classifier that is not discriminatory against a group of individuals. In the literature, this problem is often formulated as a constrained optimization problem and solved using relaxations of the fairness constraints. We show that many existing relaxations are unsatisfactory: even if a model satisfies the relaxed constraint, it can be surprisingly unfair. We propose a principled framework to solve this problem. This new approach uses a strongly convex formulation and comes with theoretical guarantees on the fairness of its solution. In practice, we show that this method gives promising results on real data.