Group Fairness in Adaptive Submodular Maximization

In this paper, we study the classic submodular maximization problem subject to a group fairness 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 some particular groups. This motivates us to study the fair submodular maximization problem, where we aim to select a group of items to maximize a (possibly non-monotone) submodular utility function subject to a group fairness 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.