User-Level Differentially Private Learning via Correlated SamplingDownload PDF

21 May 2021, 20:48 (edited 21 Jan 2022)NeurIPS 2021 PosterReaders: Everyone
  • Keywords: User-level privacy, Global stability, Representation dimension, Correlated sampling
  • TL;DR: User-level private learning is possible with very few users provided each user has sufficiently many samples.
  • 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 nearly-matching lower bound on the number of users required. A crucial component of our results is a generalization of global stability [Bun, Livni, Moran, 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.
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