On Learning and Refutation in Noninteractive Local Differential Privacy

Abstract

We study two basic statistical tasks in non-interactive local differential privacy (LDP): *learning* and *refutation*: learning requires finding a concept that best fits an unknown target function (from labelled samples drawn from a distribution), whereas refutation requires distinguishing between data distributions that are well-correlated with some concept in the class, versus distributions where the labels are random. Our main result is a complete characterization of the sample complexity of agnostic PAC learning for non-interactive LDP protocols. We show that the optimal sample complexity for any concept class is captured by the approximate $\gamma_2$ norm of a natural matrix associated with the class. Combined with previous work, this gives an *equivalence* between agnostic learning and refutation in the agnostic setting.

PDF NeurIPS OpenReview Semantic Scholar

Cite

Text

Edmonds et al. "On Learning and Refutation in Noninteractive Local Differential Privacy." Neural Information Processing Systems, 2022.

Markdown

[Edmonds et al. "On Learning and Refutation in Noninteractive Local Differential Privacy." Neural Information Processing Systems, 2022.](https://mlanthology.org/neurips/2022/edmonds2022neurips-learning/)

BibTeX

@inproceedings{edmonds2022neurips-learning,
  title     = {{On Learning and Refutation in Noninteractive Local Differential Privacy}},
  author    = {Edmonds, Alexander and Nikolov, Aleksandar and Pitassi, Toniann},
  booktitle = {Neural Information Processing Systems},
  year      = {2022},
  url       = {https://mlanthology.org/neurips/2022/edmonds2022neurips-learning/}
}