On Learning and Refutation in Noninteractive Local Differential PrivacyDownload PDF

Published: 31 Oct 2022, Last Modified: 15 Oct 2022NeurIPS 2022 AcceptReaders: Everyone
Keywords: differential privacy, local privacy, agnostic learning, refutation, non-interactive
TL;DR: We characterize the sample complexity of agnostic learning under non-interactive local differential privacy, and prove it's equivalent to refutation.
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.
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