arXiv:2407.04804v1 Announce Type: new
Abstract: 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 $f:2^Utomathbb{R}_{ge 0}$, a threshold $tau$, the goal is to find a balanced subset of $S$ with minimum cardinality such that $f(S)getau$. We first introduce discrete algorithms for FSC that achieve a bicriteria approximation ratio of $(frac{1}{epsilon}, 1-O(epsilon))$. We then present a continuous algorithm that achieves a $(lnfrac{1}{epsilon}, 1-O(epsilon))$-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.
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