Differentially Private Decomposable Submodular Maximization
Anamay Chaturvedi, Huy Lê Nguyễn, Lydia Zakynthinou · AAAI Publications (The Association for the Advancement of Artificial Intelligence (AAAI)) · 2021
We study the problem of differentially private constrained maximization of decomposable submodular functions. A submodular function is decomposable if it takes the form of a sum of submodular functions. The special case of maximizing a monotone, decomposable submodular function under cardinality constraints is known as the Combinatorial Public Projects (CPP) problem (Papadimitriou, Schapira, and Singer 2008). Previous work by Gupta et al. (2010) gave a differentially private algorithm for the CPP problem. We extend this work by designing differentially private algorithms for both monotone and non-monotone decomposable submodular maximization under general matroid constraints, with competitive utility guarantees. We complement our theoretical bounds with experiments demonstrating improved empirical performance.