Differentially Private Decomposable Submodular Maximization
This work addresses privacy-preserving optimization in machine learning and data analysis, offering incremental improvements over existing differentially private methods for submodular maximization.
The paper tackles differentially private constrained maximization of decomposable submodular functions, extending previous work to handle both monotone and non-monotone cases under general matroid constraints with competitive utility guarantees, and shows empirical performance close to non-private algorithms.
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.