cpSGD: Communication-efficient and differentially-private distributed SGD

TL;DR

This paper introduces cpSGD, a distributed stochastic gradient descent algorithm that simultaneously achieves communication efficiency and differential privacy, suitable for mobile device clients in distributed learning.

Contribution

The paper proposes a novel algorithm, cpSGD, that combines communication efficiency with differential privacy guarantees in distributed SGD settings.

Findings

Uses O(log log(nd)) bits per client per coordinate

Ensures constant privacy across clients

Improves analysis of the Binomial mechanism for privacy and utility

Abstract

Distributed stochastic gradient descent is an important subroutine in distributed learning. A setting of particular interest is when the clients are mobile devices, where two important concerns are communication efficiency and the privacy of the clients. Several recent works have focused on reducing the communication cost or introducing privacy guarantees, but none of the proposed communication efficient methods are known to be privacy preserving and none of the known privacy mechanisms are known to be communication efficient. To this end, we study algorithms that achieve both communication efficiency and differential privacy. For $d$ variables and $n \approx d$ clients, the proposed method uses $O(\log \log(nd))$ bits of communication per client per coordinate and 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 independent interest.