Federated Learning (FL) makes a large amount of edge computing devices (e.g., mobile phones) jointly learn a global model without data sharing. In FL, data are generated in a decentralized manner with high heterogeneity. This paper studies how to perform statistical estimation and inference in the federated setting. We analyze the so-called Local SGD, a multi-round estimation procedure that uses intermittent communication to improve communication efficiency. We first establish a {\it functional central limit theorem} that shows the averaged iterates of Local SGD weakly converge to a rescaled Brownian motion. We next provide two iterative inference methods: the {\it plug-in} and the {\it random scaling}. Random scaling constructs an asymptotically pivotal statistic for inference by using the information along the whole Local SGD path. Both the methods are communication efficient and applicable to online data. Our theoretical and empirical results show that Local SGD simultaneously achieves both statistical efficiency and communication efficiency.

翻译：联邦学习(FL) 联合学习大量边缘计算设备(如移动电话), 共同学习一个没有数据共享的全球模型。 在FL, 数据是以分散方式生成的, 并且具有高度异质性。 本文研究如何在联盟环境中进行统计估计和推论。 我们分析了所谓的本地 SGD, 这是一种利用间歇通信来提高通信效率的多层次估计程序。 我们首先建立了一个 ~ it 功能中心参数, 显示本地 SGD 的平均循环微弱地汇集到一个重新标定的布朗运动中。 我们接下来提供两种迭接推法: ~ 插入 和 ~ 随机缩放 。 随机缩放构建了一个无源的关键统计, 通过使用整个本地 SGD 路径的信息来推断。 这两种方法都是通信效率和适用于在线数据。 我们的理论和经验结果表明, 本地 SGD 同时实现了统计效率和通信效率 。