Group fairness in non-monotone submodular maximization

• Published in: Journal of combinatorial optimization Vol. 45; no. 3
• Main Authors: Yuan, Jing, Tang, Shaojie
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2023; Springer Nature B.V
• Subjects: Algorithms; Combinatorics; Convex and Discrete Geometry; Data mining; Decision making; Machine learning; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Maximization; Operations Research/Decision Theory; Optimization; S.I. : AAIM 2022; Theory of Computation; Approximation algorithm; Submodular optimization; Group fairness
• ISSN: 1382-6905; 1573-2886
• DOI: 10.1007/s10878-023-01019-4

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 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.