User-Level Private Learning via Correlated Sampling

TL;DR

This paper introduces a new approach for user-level differential privacy in machine learning, demonstrating that with enough samples per user, learning can be achieved with significantly fewer users than traditional methods.

Contribution

It presents a novel correlated sampling technique that enhances global stability under public randomness, enabling efficient user-level private learning with tight bounds.

Findings

Achieves learning with O(log(1/δ)/ε) users for (ε, δ)-DP.

Learns with O_ε(d) users in the local model for ε-DP.

Provides nearly-matching lower bounds on user requirements.

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 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.