# Differentially Private Learning of Geometric Concepts

## TL;DR

This paper introduces differentially private algorithms for efficiently learning unions of polygons in the plane, achieving PAC learning and privacy guarantees with a sample size depending on the number of edges and domain size.

## Contribution

It provides the first differentially private algorithms for learning unions of polygons with theoretical guarantees on sample complexity.

## Key findings

- Achieves $(eta,eta)$-PAC learning with privacy guarantees.
- Sample complexity scales with the number of edges and domain size.
- Algorithms are efficient and applicable to non-convex polygon unions.

## Abstract

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 $\tilde{O}\left(\frac{1}{\alpha\epsilon}k\log d\right)$, where the domain is $[d]\times[d]$ and $k$ is the number of edges in the union of polygons.