An $\tilde{O}$ptimal Differentially Private Learner for Concept Classes with VC Dimension 1

TL;DR

This paper introduces a nearly optimal differentially private PAC learner specifically designed for concept classes with VC dimension 1 and Littlestone dimension d, achieving a sample complexity close to the theoretical lower bound.

Contribution

The paper presents the first nearly optimal differentially private PAC learner for VC dimension 1 classes, significantly improving previous bounds.

Findings

Achieves sample complexity of $ ilde{O}( ext{log}^* d)$

Nearly matches the lower bound of $ ext{Omega}( ext{log}^* d)$

Improves upon previous upper bounds for general VC classes

Abstract

We present the first nearly optimal differentially private PAC learner for any concept class with VC dimension 1 and Littlestone dimension $d$. Our algorithm achieves the sample complexity of $\tilde{O}_{\varepsilon,\delta,\alpha,\delta}(\log^* d)$, nearly matching the lower bound of $\Omega(\log^* d)$ proved by Alon et al. [STOC19]. Prior to our work, the best known upper bound is $\tilde{O}(VC\cdot d^5)$ for general VC classes, as shown by Ghazi et al. [STOC21].