A Fast and Flat Federated Learning Method via Weighted Momentum and Sharpness-Aware Minimization

TL;DR

This paper introduces FedWMSAM, a federated learning method that combines weighted momentum and sharpness-aware minimization to improve convergence speed and generalization in non-IID settings, addressing key structural issues.

Contribution

The paper proposes a novel FedWMSAM algorithm that jointly addresses local-global curvature misalignment and momentum-echo oscillation in federated learning, with theoretical convergence guarantees.

Findings

FedWMSAM outperforms existing methods in convergence speed.

The method achieves better generalization on non-IID data.

Experimental results validate robustness and effectiveness.

Abstract

In federated learning (FL), models must \emph{converge quickly} under tight communication budgets while \emph{generalizing} across non-IID client distributions. These twin requirements have naturally led to two widely used techniques: client/server \emph{momentum} to accelerate progress, and \emph{sharpness-aware minimization} (SAM) to prefer flat solutions. However, simply combining momentum and SAM leaves two structural issues unresolved in non-IID FL. We identify and formalize two failure modes: \emph{local-global curvature misalignment} (local SAM directions need not reflect the global loss geometry) and \emph{momentum-echo oscillation} (late-stage instability caused by accumulated momentum). To our knowledge, these failure modes have not been jointly articulated and addressed in the FL literature. We propose \textbf{FedWMSAM} to address both failure modes. First, we construct a momentum-guided global perturbation from server-aggregated momentum to align clients' SAM directions with the global descent geometry, enabling a \emph{single-backprop} SAM approximation that preserves efficiency. Second, we couple momentum and SAM via a cosine-similarity adaptive rule, yielding an early-momentum, late-SAM two-phase training schedule. We provide a non-IID convergence bound that \emph{explicitly models the perturbation-induced variance} $\sigma_\rho^2=\sigma^2+(L\rho)^2$ and its dependence on $(S, K, R, N)$ on the theory side. We conduct extensive experiments on multiple datasets and model architectures, and the results validate the effectiveness, adaptability, and robustness of our method, demonstrating its superiority in addressing the optimization challenges of Federated Learning. Our code is available at https://github.com/Huang-Yongzhi/NeurlPS_FedWMSAM.