Large Stepsizes Federated Learning on Logistic Regression with Linearly Separable Data: The Case of Heterogeneous Devices

Abstract:This paper revisits the distributed learning problem for training a multinomial logistic regression model with the Federated Averaging ($\texttt{FedAvg}$) algorithm. We concentrate on a scenario with arbitrarily large stepsizes and heterogeneous update rules where the devices may perform a different number of local updates in each round. We show that, with linearly separable data, $\texttt{FedAvg}$ is stable with any stepsizes and the objective values converge to zero at the rate of ${\cal O}(1/R)$, where $R$ is the number of communication rounds. Our result also demonstrates that the effects of device heterogeneity vanish asymptotically. For sufficiently large $R$, the objective values decrease monotonically and is bounded by ${\cal O}( 1 / (R T_{\rm avg}))$, where $T_{\rm avg}$ is the average number of local update steps per communication round across devices. Numerical experiments support our findings.

Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2610.05915 [cs.LG]

(or arXiv:2610.05915v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.05915 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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