Lexicographically Fair Learning: Algorithms and Generalization

TL;DR

This paper introduces lexicographically fair learning, extending minimax fairness to prioritize fairness across multiple groups, and provides algorithms and generalization guarantees for this new fairness notion.

Contribution

It formalizes lexicographic minimax fairness, develops efficient algorithms for approximate solutions, and establishes generalization bounds for the proposed fairness criterion.

Findings

Algorithms are efficient for convex ERM problems.

Approximate lexifairness generalizes well from training to true distribution.

New definitions avoid instability issues of naive approaches.

Abstract

We extend the notion of minimax fairness in supervised learning problems to its natural conclusion: lexicographic minimax fairness (or lexifairness for short). Informally, given a collection of demographic groups of interest, minimax fairness asks that the error of the group with the highest error be minimized. Lexifairness goes further and asks that amongst all minimax fair solutions, the error of the group with the second highest error should be minimized, and amongst all of those solutions, the error of the group with the third highest error should be minimized, and so on. Despite its naturalness, correctly defining lexifairness is considerably more subtle than minimax fairness, because of inherent sensitivity to approximation error. We give a notion of approximate lexifairness that avoids this issue, and then derive oracle-efficient algorithms for finding approximately lexifair solutions in a very general setting. When the underlying empirical risk minimization problem absent fairness constraints is convex (as it is, for example, with linear and logistic regression), our algorithms are provably efficient even in the worst case. Finally, we show generalization bounds -- approximate lexifairness on the training sample implies approximate lexifairness on the true distribution with high probability. Our ability to prove generalization bounds depends on our choosing definitions that avoid the instability of naive definitions.