Concurrent Shuffle Differential Privacy Under Continual Observation

TL;DR

This paper introduces the concurrent shuffle model of differential privacy, demonstrating that multiple shufflers can significantly improve error bounds in private continual summation and bandit problems compared to a single shuffler.

Contribution

The paper proposes the concurrent shuffle model, providing tight error bounds for private summation with multiple shufflers and applying it to improve regret bounds in contextual linear bandits.

Findings

Error bound $ ilde{O}(n^{1/(2k+1)})$ with $k$ shufflers

Polylogarithmic error for $k= ext{log} n$ shufflers

Optimal $ ilde{O}( ext{sqrt}(n))$ regret with $ ext{log} n$ shufflers

Abstract

We introduce the concurrent shuffle model of differential privacy. In this model we have multiple concurrent shufflers permuting messages from different, possibly overlapping, batches of users. Similarly to the standard (single) shuffle model, the privacy requirement is that the concatenation of all shuffled messages should be differentially private. We study the private continual summation problem (a.k.a. the counter problem) and show that the concurrent shuffle model allows for significantly improved error compared to a standard (single) shuffle model. Specifically, we give a summation algorithm with error $\tilde{O}(n^{1/(2k+1)})$ with $k$ concurrent shufflers on a sequence of length $n$. Furthermore, we prove that this bound is tight for any $k$, even if the algorithm can choose the sizes of the batches adaptively. For $k=\log n$ shufflers, the resulting error is polylogarithmic, much better than $\tilde{\Theta}(n^{1/3})$ which we show is the smallest possible with a single shuffler. We use our online summation algorithm to get algorithms with improved regret bounds for the contextual linear bandit problem. In particular we get optimal $\tilde{O}(\sqrt{n})$ regret with $k= \tilde{\Omega}(\log n)$ concurrent shufflers.