Shuffle Private Stochastic Convex Optimization
This work addresses privacy-preserving machine learning for convex optimization, offering incremental improvements over prior shuffle privacy methods by enabling interactive protocols and better loss bounds.
The paper tackles the problem of stochastic convex optimization under shuffle privacy, where users send randomized messages to a shuffler to ensure differential privacy. It introduces interactive protocols that achieve loss guarantees significantly better than the local model and sometimes match the central model, with improvements demonstrated through specific algorithms like mini-batch SGD and accelerated gradient descent.
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.