Muffliato: Peer-to-Peer Privacy Amplification for Decentralized Optimization and Averaging

TL;DR

This paper introduces pairwise network differential privacy to better quantify privacy in decentralized optimization, showing that privacy guarantees improve with graph distance and matching centralized privacy-utility trade-offs.

Contribution

It formalizes pairwise network differential privacy and analyzes its amplification in decentralized optimization algorithms with gossip protocols.

Findings

Privacy guarantees increase with node distance in the graph

Algorithms match centralized privacy-utility trade-offs up to graph-dependent factors

Experimental results confirm privacy amplification in real-world datasets

Abstract

Decentralized optimization is increasingly popular in machine learning for its scalability and efficiency. Intuitively, it should also provide better privacy guarantees, as nodes only observe the messages sent by their neighbors in the network graph. But formalizing and quantifying this gain is challenging: existing results are typically limited to Local Differential Privacy (LDP) guarantees that overlook the advantages of decentralization. In this work, we introduce pairwise network differential privacy, a relaxation of LDP that captures the fact that the privacy leakage from a node $u$ to a node $v$ may depend on their relative position in the graph. We then analyze the combination of local noise injection with (simple or randomized) gossip averaging protocols on fixed and random communication graphs. We also derive a differentially private decentralized optimization algorithm that alternates between local gradient descent steps and gossip averaging. Our results show that our algorithms amplify privacy guarantees as a function of the distance between nodes in the graph, matching the privacy-utility trade-off of the trusted curator, up to factors that explicitly depend on the graph topology. Finally, we illustrate our privacy gains with experiments on synthetic and real-world datasets.