Statistical Estimation and Inference via Local SGD in Federated Learning

TL;DR

This paper develops statistical estimation and inference methods for federated learning using Local SGD, demonstrating both theoretical convergence and practical efficiency in decentralized, heterogeneous data settings.

Contribution

It introduces a functional central limit theorem for Local SGD and proposes two inference methods that are communication-efficient and suitable for online data.

Findings

Local SGD converges to a rescaled Brownian motion.

Proposed inference methods are communication-efficient.

Methods are effective for online, heterogeneous data.

Abstract

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.