Data similarity assumptions have traditionally been relied upon to understand the convergence behaviors of federated learning methods. Unfortunately, this approach often demands fine-tuning step sizes based on the level of data similarity. When data similarity is low, these small step sizes result in an unacceptably slow convergence speed for federated methods. In this paper, we present a novel and unified framework for analyzing the convergence of federated learning algorithms without the need for data similarity conditions. Our analysis centers on an inequality that captures the influence of step sizes on algorithmic convergence performance. By applying our theorems to well-known federated algorithms, we derive precise expressions for three widely used step size schedules: fixed, diminishing, and step-decay step sizes, which are independent of data similarity conditions. Finally, we conduct comprehensive evaluations of the performance of these federated learning algorithms, employing the proposed step size strategies to train deep neural network models on benchmark datasets under varying data similarity conditions. Our findings demonstrate significant improvements in convergence speed and overall performance, marking a substantial advancement in federated learning research.

本文提出了一种新颖而统一的框架，用于分析联邦学习算法的收敛性，无需数据相似性条件，并应用于著名联邦学习算法，得到了不依赖于数据相似性条件的固定步长、递减步长和步长衰减的精确表达，从而在变化的数据相似性条件下，显著提高了联邦学习算法的收敛速度和整体性能，标志着联邦学习研究的重大进展。

关于无需数据相似性的联邦学习算法收敛性的研究