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We introduce the Poisson Binomial mechanism (PBM), a discrete differentialprivacy mechanism for distributed mean estimation (DME) with applications tofederated learning and analytics. We provide a tight analysis of its privacyguarantees, showing that it achieves the same privacy-accuracy trade-offs asthe continuous Gaussian mechanism. Our analysis is based on a novel bound onthe R\'enyi divergence of two Poisson binomial distributions that may be ofindependent interest.  Unlike previous discrete DP schemes based on additive noise, our mechanismencodes local information into a parameter of the binomial distribution, andhence the output distribution is discrete with bounded support. Moreover, thesupport does not increase as the privacy budget $\varepsilon \rightarrow 0$ asin the case of additive schemes which require the addition of more noise toachieve higher privacy; on the contrary, the support becomes smaller as$\varepsilon \rightarrow 0$. The bounded support enables us to combine ourmechanism with secure aggregation (SecAgg), a multi-party cryptographicprotocol, without the need of performing modular clipping which results in anunbiased estimator of the sum of the local vectors. This in turn allows us toapply it in the private FL setting and provide an upper bound on theconvergence rate of the SGD algorithm. Moreover, since the support of theoutput distribution becomes smaller as $\varepsilon \rightarrow 0$, thecommunication cost of our scheme decreases with the privacy constraint$\varepsilon$, outperforming all previous distributed DP schemes based onadditive noise in the high privacy or low communication regimes.

The Poisson binomial mechanism for secure and private federated learning