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. In this work, we present interactive shuffle protocols for stochastic convex optimization. Our optimization protocols rely on a new noninteractive protocol for summing vectors of bounded $\ell_2$ norm. By combining this sum subroutine with techniques including 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.

中文翻译：

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Shuffle Private随机凸优化

在混洗隐私中，每个用户向受信任的混洗器发送一组随机消息，混洗器随机排列这些消息，并且由此产生的混洗消息集合必须满足差异隐私。该模型之前的工作主要集中在使用单轮通信来计算算法原语（如均值、直方图和计数）的协议。在这项工作中，我们提出了用于随机凸优化的交互式洗牌协议。我们的优化协议依赖于一种新的非交互式协议，用于对有界 $\ell_2$ 范数的向量求和。通过将这个 sum 子程序与包括小批量随机梯度下降、加速梯度下降和 Nesterov 平滑方法在内的技术相结合，