Group Fairness in Non-monotone Submodular Maximization

TL;DR

This paper introduces the first constant-factor approximation algorithms for non-monotone submodular maximization problems with group fairness constraints, ensuring representative data selection while optimizing a submodular function.

Contribution

It proposes novel algorithms for fair non-monotone submodular maximization, addressing both group fairness and global size constraints.

Findings

Developed the first constant-factor approximation algorithms.

Extended models to include global size constraints.

Applicable to data summarization with fairness considerations.

Abstract

Maximizing a submodular function has a wide range of applications in machine learning and data mining. One such application is data summarization whose goal is to select a small set of representative and diverse data items from a large dataset. However, data items might have sensitive attributes such as race or gender, in this setting, it is important to design \emph{fairness-aware} algorithms to mitigate potential algorithmic bias that may cause over- or under- representation of particular groups. Motivated by that, we propose and study the classic non-monotone submodular maximization problem subject to novel group fairness constraints. Our goal is to select a set of items that maximizes a non-monotone submodular function, while ensuring that the number of selected items from each group is proportionate to its size, to the extent specified by the decision maker. We develop the first constant-factor approximation algorithms for this problem. We also extend the basic model to incorporate an additional global size constraint on the total number of selected items.