Characterizing the Accuracy-Communication-Privacy Trade-off in Distributed Stochastic Convex Optimization
This work addresses the challenge of balancing privacy, communication efficiency, and accuracy in distributed machine learning, providing a foundational characterization for researchers and practitioners in privacy-preserving AI.
The paper tackles the problem of differentially private stochastic convex optimization in a distributed setting with multiple clients, establishing matching lower and upper bounds to characterize the trade-off between accuracy, communication, and privacy.
We consider the problem of differentially private stochastic convex optimization (DP-SCO) in a distributed setting with $M$ clients, where each of them has a local dataset of $N$ i.i.d. data samples from an underlying data distribution. The objective is to design an algorithm to minimize a convex population loss using a collaborative effort across $M$ clients, while ensuring the privacy of the local datasets. In this work, we investigate the accuracy-communication-privacy trade-off for this problem. We establish matching converse and achievability results using a novel lower bound and a new algorithm for distributed DP-SCO based on Vaidya's plane cutting method. Thus, our results provide a complete characterization of the accuracy-communication-privacy trade-off for DP-SCO in the distributed setting.