Fair Submodular Cover

Submodular optimization is a fundamental problem with many applications in machine learning, often involving decision-making over datasets with sensitive attributes such as gender or age. In such settings, it is often desirable to produce a diverse solution set that is fairly distributed with respect to these attributes. Motivated by this, we initiate the study of Fair Submodular Cover (FSC), where given a ground set U, a monotone submodular function f: 2U ₀, a threshold, the goal is to find a balanced subset of S with minimum cardinality such that f (S). We first introduce discrete algorithms for FSC that achieve a bicriteria approximation ratio of (1, 1-O () ). We then present a continuous algorithm that achieves a (1, 1-O () ) -bicriteria approximation ratio, which matches the best approximation guarantee of submodular cover without a fairness constraint. Finally, we complement our theoretical results with a number of empirical evaluations that demonstrate the effectiveness of our algorithms on instances of maximum coverage.