A Unified Framework for Analyzing and Optimizing a Class of Convex Fairness Measures

TL;DR

This paper introduces a unified, convex framework for analyzing and optimizing a broad class of fairness measures, enabling more efficient and stable fairness-aware optimization solutions.

Contribution

It develops a dual representation and geometric characterization of convex fairness measures, unifies their optimization, and demonstrates improved computational efficiency and stability.

Findings

Unified mathematical expression for convex fairness measures

Dual representation as robustified order-based measures

Numerical results show computational efficiency and stability benefits

Abstract

We propose a new framework that unifies different fairness measures into a general, parameterized class of convex fairness measures suitable for optimization contexts. First, we propose a new class of order-based fairness measures, discuss their properties, and derive an axiomatic characterization for such measures. Then, we introduce the class of convex fairness measures, discuss their properties, and derive an equivalent dual representation of these measures as a robustified order-based fairness measure over their dual sets. Importantly, this dual representation renders a unified mathematical expression and an alternative geometric characterization for convex fairness measures through their dual sets. Moreover, it allows us to develop a unified framework for optimization problems with a convex fairness measure objective or constraint, including unified reformulations and solution methods. In addition, we provide stability results that quantify the impact of employing different convex fairness measures on the optimal value and solution of the resulting fairness-promoting optimization problem. Finally, we present numerical results demonstrating the computational efficiency of our unified framework over traditional ones and illustrating our stability results.