UserLevel Private Learning via Correlated Sampling
Abstract
Most works in learning with differential privacy (DP) have focused on the setting where each user has a single sample. In this work, we consider the setting where each user holds $m$ samples and the privacy protection is enforced at the level of each user's data. We show that, in this setting, we may learn with a much fewer number of users. Specifically, we show that, as long as each user receives sufficiently many samples, we can learn any privately learnable class via an $(\epsilon, \delta)$DP algorithm using only $O(\log(1/\delta)/\epsilon)$ users. For $\epsilon$DP algorithms, we show that we can learn using only $O_{\epsilon}(d)$ users even in the local model, where $d$ is the probabilistic representation dimension. In both cases, we show a nearlymatching lower bound on the number of users required. A crucial component of our results is a generalization of global stability [Bun et al., FOCS 2020] that allows the use of public randomness. Under this relaxed notion, we employ a correlated sampling strategy to show that the global stability can be boosted to be arbitrarily close to one, at a polynomial expense in the number of samples.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.11208
 Bibcode:
 2021arXiv211011208G
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Cryptography and Security;
 Computer Science  Data Structures and Algorithms
 EPrint:
 To appear in NeurIPS 2021