Delay Analysis of Wireless Federated Learning Based on Saddle Point Approximation and Large Deviation Theory

TL;DR

This paper develops a unified mathematical framework using saddle point approximation, EVT, and LDT to analyze the delay distribution in wireless federated learning over fading channels, addressing a key challenge for delay-sensitive applications.

Contribution

It introduces a novel approach combining saddle point approximation, EVT, and LDT to accurately estimate delay distributions in wireless FL, including tail behavior.

Findings

Approximation error decreases as training accuracy improves.

The framework effectively characterizes delay tail distributions.

Simulation results confirm the accuracy of the proposed method.

Abstract

Federated learning (FL) is a collaborative machine learning paradigm, which enables deep learning model training over a large volume of decentralized data residing in mobile devices without accessing clients' private data. Driven by the ever increasing demand for model training of mobile applications or devices, a vast majority of FL tasks are implemented over wireless fading channels. Due to the time-varying nature of wireless channels, however, random delay occurs in both the uplink and downlink transmissions of FL. How to analyze the overall time consumption of a wireless FL task, or more specifically, a FL's delay distribution, becomes a challenging but important open problem, especially for delay-sensitive model training. In this paper, we present a unified framework to calculate the approximate delay distributions of FL over arbitrary fading channels. Specifically, saddle point approximation, extreme value theory (EVT), and large deviation theory (LDT) are jointly exploited to find the approximate delay distribution along with its tail distribution, which characterizes the quality-of-service of a wireless FL system. Simulation results will demonstrate that our approximation method achieves a small approximation error, which vanishes with the increase of training accuracy.