Momentum Benefits Non-IID Federated Learning Simply and Provably

TL;DR

This paper demonstrates that incorporating momentum into federated learning algorithms like FedAvg and SCAFFOLD improves convergence, especially under data heterogeneity and partial participation, with provable guarantees and state-of-the-art results.

Contribution

It introduces momentum-based enhancements for FedAvg and SCAFFOLD, enabling convergence without bounded heterogeneity assumptions and improving convergence rates.

Findings

Momentum allows FedAvg to converge without bounded heterogeneity.

Momentum enables SCAFFOLD to converge faster under partial participation.

New variance-reduced methods achieve state-of-the-art convergence rates.

Abstract

Federated learning is a powerful paradigm for large-scale machine learning, but it faces significant challenges due to unreliable network connections, slow communication, and substantial data heterogeneity across clients. FedAvg and SCAFFOLD are two prominent algorithms to address these challenges. In particular, FedAvg employs multiple local updates before communicating with a central server, while SCAFFOLD maintains a control variable on each client to compensate for ``client drift'' in its local updates. Various methods have been proposed to enhance the convergence of these two algorithms, but they either make impractical adjustments to the algorithmic structure or rely on the assumption of bounded data heterogeneity. This paper explores the utilization of momentum to enhance the performance of FedAvg and SCAFFOLD. When all clients participate in the training process, we demonstrate that incorporating momentum allows FedAvg to converge without relying on the assumption of bounded data heterogeneity even using a constant local learning rate. This is novel and fairly surprising as existing analyses for FedAvg require bounded data heterogeneity even with diminishing local learning rates. In partial client participation, we show that momentum enables SCAFFOLD to converge provably faster without imposing any additional assumptions. Furthermore, we use momentum to develop new variance-reduced extensions of FedAvg and SCAFFOLD, which exhibit state-of-the-art convergence rates. Our experimental results support all theoretical findings.