A Unified Linear Speedup Analysis of Federated Averaging and Nesterov FedAvg

TL;DR

This paper provides a unified analysis of the convergence behavior of Federated Averaging (FedAvg) and its Nesterov accelerated variant, demonstrating linear speedup in various convex settings and characterizing their convergence rates.

Contribution

It offers the first unified convergence guarantees for FedAvg and Nesterov FedAvg under non-i.i.d. data and partial participation, including linear speedup results.

Findings

FedAvg achieves linear speedup in convex and strongly convex problems.

Nesterov FedAvg has established convergence rates with linear speedup.

Empirical results support the theoretical convergence guarantees.

Abstract

Federated learning (FL) learns a model jointly from a set of participating devices without sharing each other's privately held data. The characteristics of non-i.i.d. data across the network, low device participation, high communication costs, and the mandate that data remain private bring challenges in understanding the convergence of FL algorithms, particularly regarding how convergence scales with the number of participating devices. In this paper, we focus on Federated Averaging (FedAvg), one of the most popular and effective FL algorithms in use today, as well as its Nesterov accelerated variant, and conduct a systematic study of how their convergence scale with the number of participating devices under non-i.i.d. data and partial participation in convex settings. We provide a unified analysis that establishes convergence guarantees for FedAvg under strongly convex, convex, and overparameterized strongly convex problems. We show that FedAvg enjoys linear speedup in each case, although with different convergence rates and communication efficiencies. For strongly convex and convex problems, we also characterize the corresponding convergence rates for the Nesterov accelerated FedAvg algorithm, which are the first linear speedup guarantees for momentum variants of FedAvg in convex settings. Empirical studies of the algorithms in various settings have supported our theoretical results.