Group Equality in Adaptive Submodular Maximization

Shaojie Tang () and Jing Yuan ()
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Shaojie Tang: Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, Texas 75080
Jing Yuan: Department of Computer Science and Engineering, The University of North Texas, Denton, Texas 76205

INFORMS Journal on Computing, 2024, vol. 36, issue 2, 359-376

Abstract: In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both nonadaptive and adaptive settings. It is shown that the utility function of many machine learning applications, including data summarization, influence maximization in social networks, and personalized recommendation, satisfies the property of submodularity. Hence, maximizing a submodular function subject to various constraints can be found at the heart of many of those applications. On a high level, submodular maximization aims to select a group of most representative items (e.g., data points). However, the design of most existing algorithms does not incorporate the fairness constraint, leading to underrepresentation or overrepresentation of some particular groups. This motivates us to study the submodular maximization problem with group equality, in which we aim to select a group of items to maximize a (possibly nonmonotone) submodular utility function subject to a group equality constraint. To this end, we develop the first constant-factor approximation algorithm for this problem. The design of our algorithm is robust enough to be extended to solving the submodular maximization problem under a more complicated adaptive setting. Moreover, we further extend our study to incorporating a global cardinality constraint and other fairness notations.

Keywords: submodular maximization; stochastic optimization; group fairness (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:36:y:2024:i:2:p:359-376

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