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 $(\alpha,\beta)$--probably approximately correct and $(\varepsilon,\delta)$--differentially using a sample size $\tilde{O}\left(\frac{1}{\alpha\varepsilon}k\log d\right)$, where domain is $[d]\times[d]$ $k$ number edges union polygons. obtained by designing variant classical (nonprivate) learner conjunctions greedy algorithm set cover.