Differentially Private Decomposable Submodular Maximization

TL;DR

This paper develops differentially private algorithms for maximizing decomposable submodular functions under various constraints, improving utility guarantees and demonstrating strong empirical performance compared to non-private methods.

Contribution

It introduces new differentially private algorithms for both monotone and non-monotone decomposable submodular maximization under general matroid constraints, extending prior work.

Findings

Algorithms achieve competitive utility guarantees.

Empirical results outperform previous private algorithms.

Performance approaches non-private algorithms.

Abstract

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 et al., 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 empirical performance, which improves over the differentially private algorithms for the general case of submodular maximization and is close to the performance of non-private algorithms.