Renyi Differential Privacy in the Shuffle Model: Enhanced Amplification Bounds
E Chen, Yang Cao, Yifei Ge
TL;DR
This work advances Renyi Differential Privacy in the shuffle model by providing the first asymptotically optimal RDP analysis without restricting the local privacy budget $ε_0$, and by linking the shuffle process to a multinomial distance whose exact and asymptotic bounds yield tighter privacy guarantees. The authors introduce a hypothesis-testing framework to derive exact and asymptotic RDP bounds and show the shuffled mechanism closely matches low-loss GDP/regression bounds in the limit. They also present a DP-SGD algorithm built on these RDP insights, with experimental results on MNIST demonstrating improved privacy-utility performance over existing shuffle-based approaches at the same privacy level. Overall, the paper tightens the theoretical understanding of privacy amplification via shuffling and provides practical, scalable guidance for privacy-preserving learning. The combination of a multinomial-based exact bound, an asymptotic normal-approximation bound, and a hypothesis-testing toolkit represents a cohesive advancement with direct impact on private distributed learning workflows.
Abstract
The shuffle model of Differential Privacy (DP) has gained significant attention in privacy-preserving data analysis due to its remarkable tradeoff between privacy and utility. It is characterized by adding a shuffling procedure after each user's locally differentially private perturbation, which leads to a privacy amplification effect, meaning that the privacy guarantee of a small level of noise, say $ε_0$, can be enhanced to $O(ε_0/\sqrt{n})$ (the smaller, the more private) after shuffling all $n$ users' perturbed data. Most studies in the shuffle DP focus on proving a tighter privacy guarantee of privacy amplification. However, the current results assume that the local privacy budget $ε_0$ is within a limited range. In addition, there remains a gap between the tightest lower bound and the known upper bound of the privacy amplification. In this work, we push forward the state-of-the-art by making the following contributions. Firstly, we present the first asymptotically optimal analysis of Renyi Differential Privacy (RDP) in the shuffle model without constraints on $ε_0$. Secondly, we introduce hypothesis testing for privacy amplification through shuffling, offering a distinct analysis technique and a tighter upper bound. Furthermore, we propose a DP-SGD algorithm based on RDP. Experiments demonstrate that our approach outperforms existing methods significantly at the same privacy level.