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Distributed stochastic gradient descent is an important subroutine indistributed learning. A setting of particular interest is when the clients aremobile devices, where two important concerns are communication efficiency andthe privacy of the clients. Several recent works have focused on reducing thecommunication cost or introducing privacy guarantees, but none of the proposedcommunication efficient methods are known to be privacy preserving and none ofthe known privacy mechanisms are known to be communication efficient. To thisend, we study algorithms that achieve both communication efficiency anddifferential privacy. For $d$ variables and $n \approx d$ clients, the proposedmethod uses $O(\log \log(nd))$ bits of communication per client per coordinateand ensures constant privacy.  We also extend and improve previous analysis of the \emph{Binomial mechanism}showing that it achieves nearly the same utility as the Gaussian mechanism,while requiring fewer representation bits, which can be of independentinterest.

cpSGD: Communication-efficient and differentially-private distributed SGD