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arXiv · 2505.06581

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

Chao Yan
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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].

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Chao Yan. 2025-05-10. An $\tilde{O}$ptimal Differentially Private Learner for Concept Classes with VC Dimension 1. https://arxiv.org/abs/2505.06581

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