Private PAC Learning May be Harder than Online Learning
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929246484561920 |
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| author | Bun, Mark Cohen, Aloni Desai, Rathin |
| author_facet | Bun, Mark Cohen, Aloni Desai, Rathin |
| contents | We continue the study of the computational complexity of differentially private PAC learning and how it is situated within the foundations of machine learning. A recent line of work uncovered a qualitative equivalence between the private PAC model and Littlestone's mistake-bounded model of online learning, in particular, showing that any concept class of Littlestone dimension $d$ can be privately PAC learned using $\mathrm{poly}(d)$ samples. This raises the natural question of whether there might be a generic conversion from online learners to private PAC learners that also preserves computational efficiency.
We give a negative answer to this question under reasonable cryptographic assumptions (roughly, those from which it is possible to build indistinguishability obfuscation for all circuits). We exhibit a concept class that admits an online learner running in polynomial time with a polynomial mistake bound, but for which there is no computationally-efficient differentially private PAC learner. Our construction and analysis strengthens and generalizes that of Bun and Zhandry (TCC 2016-A), who established such a separation between private and non-private PAC learner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11119 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Private PAC Learning May be Harder than Online Learning Bun, Mark Cohen, Aloni Desai, Rathin Machine Learning Cryptography and Security Data Structures and Algorithms We continue the study of the computational complexity of differentially private PAC learning and how it is situated within the foundations of machine learning. A recent line of work uncovered a qualitative equivalence between the private PAC model and Littlestone's mistake-bounded model of online learning, in particular, showing that any concept class of Littlestone dimension $d$ can be privately PAC learned using $\mathrm{poly}(d)$ samples. This raises the natural question of whether there might be a generic conversion from online learners to private PAC learners that also preserves computational efficiency. We give a negative answer to this question under reasonable cryptographic assumptions (roughly, those from which it is possible to build indistinguishability obfuscation for all circuits). We exhibit a concept class that admits an online learner running in polynomial time with a polynomial mistake bound, but for which there is no computationally-efficient differentially private PAC learner. Our construction and analysis strengthens and generalizes that of Bun and Zhandry (TCC 2016-A), who established such a separation between private and non-private PAC learner. |
| title | Private PAC Learning May be Harder than Online Learning |
| topic | Machine Learning Cryptography and Security Data Structures and Algorithms |
| url | https://arxiv.org/abs/2402.11119 |