Improved Algorithms for Fair Matroid Submodular Maximization

TL;DR

This paper introduces a new algorithm for fair matroid submodular maximization that nearly enforces perfect fairness while maintaining a constant approximation ratio, improving over previous relaxed fairness guarantees.

Contribution

The authors develop an algorithm that achieves arbitrarily close to full fairness with a constant-factor approximation, advancing the state-of-the-art in fair submodular maximization under matroid constraints.

Findings

Algorithm achieves near-perfect fairness with only a small loss.

Empirical results show effectiveness on real-world datasets.

Method outperforms previous relaxed fairness algorithms.

Abstract

Submodular maximization subject to matroid constraints is a central problem with many applications in machine learning. As algorithms are increasingly used in decision-making over datapoints with sensitive attributes such as gender or race, it is becoming crucial to enforce fairness to avoid bias and discrimination. Recent work has addressed the challenge of developing efficient approximation algorithms for fair matroid submodular maximization. However, the best algorithms known so far are only guaranteed to satisfy a relaxed version of the fairness constraints that loses a factor 2, i.e., the problem may ask for $\ell$ elements with a given attribute, but the algorithm is only guaranteed to find $\lfloor \ell/2 \rfloor$. In particular, there is no provable guarantee when $\ell=1$, which corresponds to a key special case of perfect matching constraints. In this work, we achieve a new trade-off via an algorithm that gets arbitrarily close to full fairness. Namely, for any constant $\varepsilon>0$, we give a constant-factor approximation to fair monotone matroid submodular maximization that in expectation loses only a factor $(1-\varepsilon)$ in the lower-bound fairness constraint. Our empirical evaluation on a standard suite of real-world datasets -- including clustering, recommendation, and coverage tasks -- demonstrates the practical effectiveness of our methods.