  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
$f:2^U\to\mathbb{R}_{\ge 0}$, a threshold $\tau$, the goal is to find a
balanced subset of $S$ with minimum cardinality such that $f(S)\ge\tau$. 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 $(\ln\frac{1}{\epsilon},
1-O(\epsilon))$-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.
