DIFFERENTIALLY PRIVATE LEARNING OF GEOMETRIC CONCEPTS

We present efficient differentially private algorithms for learning unions of polygons in the plane (which are not necessarily convex). Our algorithms are (α , β)-probably approximately correct and (ϵ , δ )-differentially private using a sample of size O ( 1 α) , where the domain is [d] × [d] and k is the number of edges in the union of polygons. Our algorithms are obtained by designing a private variant of the classical (nonprivate) learner for conjunctions using the greedy algorithm for set cover. © 2022 Society for Industrial and Applied Mathematics.