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We consider a federated data analytics problem in which a server coordinatesthe collaborative data analysis of multiple users with privacy concerns andlimited communication capability. The commonly adopted compression schemesintroduce information loss into local data while improving communicationefficiency, and it remains an open problem whether such discrete-valuedmechanisms provide any privacy protection. In this paper, we study the localdifferential privacy guarantees of discrete-valued mechanisms with finiteoutput space through the lens of $f$-differential privacy (DP). Morespecifically, we advance the existing literature by deriving tight $f$-DPguarantees for a variety of discrete-valued mechanisms, including the binomialnoise and the binomial mechanisms that are proposed for privacy preservation,and the sign-based methods that are proposed for data compression, inclosed-form expressions. We further investigate the amplification in privacy bysparsification and propose a ternary stochastic compressor. By leveragingcompression for privacy amplification, we improve the existing methods byremoving the dependency of accuracy (in terms of mean square error) oncommunication cost in the popular use case of distributed mean estimation,therefore breaking the three-way tradeoff between privacy, communication, andaccuracy. Finally, we discuss the Byzantine resilience of the proposedmechanism and its application in federated learning.

Breaking the Communication-Privacy-Accuracy Tradeoff with $f$-Differential Privacy