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

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].

@article{yan2025_2505.06581,
  title={ An \tilde{O}ptimal Differentially Private Learner for Concept Classes with VC Dimension 1 },
  author={ Chao Yan },
  journal={arXiv preprint arXiv:2505.06581},
  year={ 2025 }
}