📝 SummarXiv

Abstract

Gradient compression is an effective technique for reducing communication overhead in federated learning (FL), and error feedback (EF) is widely adopted to remedy the compression errors. However, in asynchronous FL settings-which inherently face three major challenges: asynchronous delay, data heterogeneity, and flexible client participation-the complex interactions among these system/statistical constraints and compression/EF mechanisms remain poorly understood theoretically. There is a significant lack of systematic convergence analysis that adequately captures these complex couplings. In this paper, we fill this gap by analyzing the convergence behaviors of FL under different frameworks. We first consider a basic asynchronous FL framework AsynFL, and establish an improved convergence analysis that relies on fewer assumptions and yields a superior convergence rate than prior studies. Then, we consider a variant framework with gradient compression, AsynFLC. We derive sufficient conditions for its convergence, indicating the nonlinear interaction between asynchronous delay and compression rate. Our analysis further demonstrates how asynchronous delay and data heterogeneity jointly amplify compression-induced errors, thereby hindering convergence. Furthermore, we study the convergence of AsynFLC-EF, the framework that further integrates EF. We prove that EF can effectively reduce the variance of gradient estimation despite asynchronous delays, which enables AsynFLC-EF to match the convergence rate of AsynFL. We also show that the impact of asynchronous delay and flexible participation on EF is limited to slowing down the higher-order convergence term. Experimental results substantiate our analytical findings very well.