Differentially Private Learning of Geometric Concepts

We present differentially private efficient algorithms for learning union of polygons in the plane (which are not necessarily convex). Our algorithms achieve $(alpha,beta)$-PAC learning and $(epsilon,delta)$-differential privacy using a sample of size $tilde{O}left(frac{1}{alphaepsilon}klog dright)$, where the domain is $[d]times[d]$ and $k$ is the number of edges in the union of polygons.