Group Equality in Adaptive Submodular Maximization

TL;DR

This paper introduces the first constant-factor approximation algorithm for submodular maximization under group equality constraints, addressing fairness issues in applications like data summarization and influence maximization, with extensions to adaptive and other fairness constraints.

Contribution

It presents a novel algorithm for group-fair submodular maximization, applicable in adaptive settings and with additional constraints, advancing fairness-aware optimization methods.

Findings

First constant-factor approximation algorithm for group equality constraints

Algorithm extends to adaptive and more complex fairness settings

Applicable to various machine learning tasks like data summarization

Abstract

In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both non-adaptive and adaptive settings. It has been 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 under- or over-representation of some particular groups. This motivates us to study the submodular maximization problem with group equality, where we aim to select a group of items to maximize a (possibly non-monotone) 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.