The Skellam Mechanism for Differentially Private Federated Learning

TL;DR

This paper introduces the Skellam mechanism, a discrete differential privacy method based on Poisson differences, suitable for federated learning with secure aggregation, offering comparable privacy-accuracy trade-offs to Gaussian mechanisms.

Contribution

The paper proposes the multi-dimensional Skellam mechanism for differential privacy, analyzing its privacy guarantees and demonstrating its practical advantages in federated learning scenarios.

Findings

Skellam mechanism matches Gaussian privacy-accuracy trade-offs.

It is computationally efficient and easy to implement.

Provides strong privacy guarantees in federated learning.

Abstract

We introduce the multi-dimensional Skellam mechanism, a discrete differential privacy mechanism based on the difference of two independent Poisson random variables. To quantify its privacy guarantees, we analyze the privacy loss distribution via a numerical evaluation and provide a sharp bound on the R\'enyi divergence between two shifted Skellam distributions. While useful in both centralized and distributed privacy applications, we investigate how it can be applied in the context of federated learning with secure aggregation under communication constraints. Our theoretical findings and extensive experimental evaluations demonstrate that the Skellam mechanism provides the same privacy-accuracy trade-offs as the continuous Gaussian mechanism, even when the precision is low. More importantly, Skellam is closed under summation and sampling from it only requires sampling from a Poisson distribution -- an efficient routine that ships with all machine learning and data analysis software packages. These features, along with its discrete nature and competitive privacy-accuracy trade-offs, make it an attractive practical alternative to the newly introduced discrete Gaussian mechanism.