The Skellam Mechanism for Differentially Private Federated Learning
This work addresses privacy and efficiency challenges in federated learning for distributed systems, offering a practical alternative to existing mechanisms.
The paper tackles the problem of implementing differentially private federated learning under communication constraints by introducing the multi-dimensional Skellam mechanism, which provides privacy-accuracy trade-offs comparable to the continuous Gaussian mechanism, as demonstrated through theoretical analysis and experiments.
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 Rényi 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.