Fairness in Submodular Maximization over a Matroid Constraint

TL;DR

This paper addresses the challenge of ensuring fairness in submodular maximization problems constrained by matroids, proposing algorithms and impossibility results to balance solution quality, fairness, and generality.

Contribution

It extends fairness considerations to submodular maximization under matroid constraints, including non-monotone objectives, filling a gap in existing research.

Findings

Proposed algorithms balancing fairness and quality

Impossibility results highlighting trade-offs

Extensions to non-monotone objectives

Abstract

Submodular maximization over a matroid constraint is a fundamental problem with various applications in machine learning. Some of these applications involve decision-making over datapoints with sensitive attributes such as gender or race. In such settings, it is crucial to guarantee that the selected solution is fairly distributed with respect to this attribute. Recently, fairness has been investigated in submodular maximization under a cardinality constraint in both the streaming and offline settings, however the more general problem with matroid constraint has only been considered in the streaming setting and only for monotone objectives. This work fills this gap. We propose various algorithms and impossibility results offering different trade-offs between quality, fairness, and generality.