On the Convergence of Federated Learning Algorithms without Data Similarity

TL;DR

This paper introduces a unified framework for analyzing federated learning convergence without relying on data similarity assumptions, enabling more robust and faster training across diverse data distributions.

Contribution

It develops a novel analysis method that removes the need for data similarity conditions and provides explicit convergence expressions for common step size schedules.

Findings

Improved convergence speed with proposed step size strategies

Effective training of neural networks on benchmark datasets

Robust performance across varying data similarity levels

Abstract

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.