On Learning and Refutation in Noninteractive Local Differential Privacy

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Bibtex Paper Supplemental


Alexander Edmonds, Aleksandar Nikolov, Toniann Pitassi


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.