Differentially Private Submodular Maximization: Data Summarization in Disguise

Many data summarization applications are captured by the general framework of submodular maximization. As a consequence, a wide range of efficient approximation algorithms have been developed. However, when such applications involve sensitive data about individuals, their privacy concerns are not automatically addressed. To remedy this problem, we propose a general and systematic study of differentially private submodular maximization. We present privacypreserving algorithms for both monotone and non-monotone submodular maximization under cardinality, matroid, and p-extendible system constraints, with guarantees that are competitive with optimal solutions. Along the way, we analyze a new algorithm for non-monotone submodular maximization under a cardinality constraint, which is the first (even non-privately) to achieve a constant approximation ratio with a linear number of function evaluations. We additionally provide two concrete experiments to validate the efficacy of these algorithms.