An $\tilde{O}$ptimal Differentially Private Learner for Concept Classes with VC Dimension 1
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908469861285888 |
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| author | Yan, Chao |
| author_facet | Yan, Chao |
| contents | 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 $\tilde{O}_{\varepsilon,δ,α,δ}(\log^* d)$, nearly matching the lower bound of $Ω(\log^* d)$ 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An $\tilde{O}$ptimal Differentially Private Learner for Concept Classes with VC Dimension 1 Yan, Chao Machine Learning Cryptography and Security 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 $\tilde{O}_{\varepsilon,δ,α,δ}(\log^* d)$, nearly matching the lower bound of $Ω(\log^* d)$ 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]. |
| title | An $\tilde{O}$ptimal Differentially Private Learner for Concept Classes with VC Dimension 1 |
| topic | Machine Learning Cryptography and Security |
| url | https://arxiv.org/abs/2505.06581 |