Composition Theorems for Interactive Differential PrivacyDownload PDF

Published: 31 Oct 2022, 18:00, Last Modified: 11 Jan 2023, 16:02NeurIPS 2022 AcceptReaders: Everyone
Keywords: Differential Privacy, Composition Theorems, Interactive mechanism
TL;DR: The optimal composition theorem still holds when the adversary interacts with several differentially private algorithms in parallel.
Abstract: An interactive mechanism is an algorithm that stores a data set and answers adaptively chosen queries to it. The mechanism is called differentially private, if any adversary cannot distinguish whether a specific individual is in the data set by interacting with the mechanism. We study composition properties of differential privacy in concurrent compositions. In this setting, an adversary interacts with $k$ interactive mechanisms in parallel and can interleave its queries to the mechanisms arbitrarily. Previously, Vadhan and Wang [2021] proved an optimal concurrent composition theorem for pure-differential privacy. We significantly generalize and extend their results. Namely, we prove optimal parallel composition properties for several major notions of differential privacy in the literature, including approximate DP, Renyi DP, and zero-concentrated DP. Our results demonstrate that the adversary gains no advantage by interleaving its queries to independently running mechanisms. Hence, interactivity is a feature that differential privacy grants us for free. Concurrently and independently of our work, Vadhan and Zhang [2022] proved an optimal concurrent composition theorem for f-DP [Dong et al., 2022], which implies our result for the approximate DP case.
Supplementary Material: pdf
24 Replies