Shuffle Private Stochastic Convex Optimization

TL;DR

This paper introduces interactive shuffle protocols for stochastic convex optimization under shuffle privacy, achieving improved loss guarantees that often match the central model, by combining a new vector summation protocol with advanced gradient methods.

Contribution

It presents the first interactive shuffle protocols for stochastic convex optimization, utilizing a novel noninteractive vector sum protocol to enhance privacy-utility trade-offs.

Findings

Protocols achieve loss guarantees close to the central model.

Significant improvements over local model privacy guarantees.

Applicable to various convex loss functions.

Abstract

In shuffle privacy, each user sends a collection of randomized messages to a trusted shuffler, the shuffler randomly permutes these messages, and the resulting shuffled collection of messages must satisfy differential privacy. Prior work in this model has largely focused on protocols that use a single round of communication to compute algorithmic primitives like means, histograms, and counts. We present interactive shuffle protocols for stochastic convex optimization. Our protocols rely on a new noninteractive protocol for summing vectors of bounded $\ell_2$ norm. By combining this sum subroutine with mini-batch stochastic gradient descent, accelerated gradient descent, and Nesterov's smoothing method, we obtain loss guarantees for a variety of convex loss functions that significantly improve on those of the local model and sometimes match those of the central model.