Minimax Optimal Fair Classification with Bounded Demographic Disparity

TL;DR

This paper establishes the fundamental limits of fair binary classification under demographic disparity constraints with finite data, and introduces a new method, FairBayes-DDP+, that achieves optimal tradeoffs.

Contribution

It derives a minimax lower bound on classification error under fairness constraints and proposes a novel algorithm that attains this bound, improving fairness-accuracy tradeoffs.

Findings

FairBayes-DDP+ controls disparity at the specified level.

The method achieves minimax optimality in fairness-aware classification.

Experiments show improved speed and tradeoff over baselines.

Abstract

Mitigating the disparate impact of statistical machine learning methods is crucial for ensuring fairness. While extensive research aims to reduce disparity, the effect of using a \emph{finite dataset} -- as opposed to the entire population -- remains unclear. This paper explores the statistical foundations of fair binary classification with two protected groups, focusing on controlling demographic disparity, defined as the difference in acceptance rates between the groups. Although fairness may come at the cost of accuracy even with infinite data, we show that using a finite sample incurs additional costs due to the need to estimate group-specific acceptance thresholds. We study the minimax optimal classification error while constraining demographic disparity to a user-specified threshold. To quantify the impact of fairness constraints, we introduce a novel measure called \emph{fairness-aware excess risk} and derive a minimax lower bound on this measure that all classifiers must satisfy. Furthermore, we propose FairBayes-DDP+, a group-wise thresholding method with an offset that we show attains the minimax lower bound. Our lower bound proofs involve several innovations. Experiments support that FairBayes-DDP+ controls disparity at the user-specified level, while being faster and having a more favorable fairness-accuracy tradeoff than several baselines.