Balancing utility and fairness in submodular maximization

• Main Authors: WANG, Yanhao, LI, Yuchen, BONCHI, Francesco, WANG, Ying
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2023
• Subjects: submodular function maximization; Bicriteria Submodular Maximization; Databases and Information Systems
• Online Access: https://ink.library.smu.edu.sg/sis_research/8467; https://ink.library.smu.edu.sg/context/sis_research/article/9470/viewcontent/paper_7.pdf
• Institution: Singapore Management University

Submodular function maximization is a fundamental combinatorial optimization problem with plenty of applications – including data summarization, influence maximization, and recommendation. In many of these problems, the goal is to find a solution that maximizes the average utility over all users, for each of whom the utility is defined by a monotone submodular function. However, when the population of users is composed of several demographic groups, another critical problem is whether the utility is fairly distributed across different groups. Although the utility and fairness objectives are both desirable, they might contradict each other, and, to the best of our knowledge, little attention has been paid to optimizing them jointly.To fill this gap, we propose a new problem called Bicriteria Submodular Maximization (BSM) to balance utility and fairness. Specifically, it requires finding a fixed-size solution to maximize the utility function, subject to the value of the fairness function not being below a threshold. Since BSM is inapproximable within any constant factor, we focus on designing efficient instancedependent approximation schemes. Our algorithmic proposal comprises two methods, with different approximation factors, obtained by converting a BSM instance into other submodular optimization problem instances. Using real-world and synthetic datasets, we showcase applications of our proposed methods in three submodular maximization problems: maximum coverage, influence maximization, and facility location.