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arXiv · 2501.03222

Characterizing the Accuracy-Communication-Privacy Trade-off in Distributed Stochastic Convex Optimization

Sudeep Salgia·Nikola Pavlovic·Yuejie Chi·Qing Zhao
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Abstract

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.

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Sudeep Salgia, Nikola Pavlovic, Yuejie Chi, Qing Zhao. 2025-01-06. Characterizing the Accuracy-Communication-Privacy Trade-off in Distributed Stochastic Convex Optimization. https://arxiv.org/abs/2501.03222

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