3 research outputs found
Differentially Private Decomposable Submodular Maximization
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