Constant Stepsize Local GD for Logistic Regression: Acceleration by Instability

• URL: http://arxiv.org/abs/2506.13974v1
• Date: Mon, 16 Jun 2025 20:29:00 GMT
• Title: Constant Stepsize Local GD for Logistic Regression: Acceleration by Instability
• Abstract summary: We analyze Local Gradient Descent for logistic regression with separable, heterogeneous data using any stepsize $eta > 0$.<n>Our analysis parallels the single machine analysis ofcitewu2024large in which instability is caused by extremely large stepsizes.
• Score: 13.332982107151434
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Existing analysis of Local (Stochastic) Gradient Descent for heterogeneous objectives requires stepsizes $\eta \leq 1/K$ where $K$ is the communication interval, which ensures monotonic decrease of the objective. In contrast, we analyze Local Gradient Descent for logistic regression with separable, heterogeneous data using any stepsize $\eta > 0$. With $R$ communication rounds and $M$ clients, we show convergence at a rate $\mathcal{O}(1/\eta K R)$ after an initial unstable phase lasting for $\widetilde{\mathcal{O}}(\eta K M)$ rounds. This improves upon the existing $\mathcal{O}(1/R)$ rate for general smooth, convex objectives. Our analysis parallels the single machine analysis of~\cite{wu2024large} in which instability is caused by extremely large stepsizes, but in our setting another source of instability is large local updates with heterogeneous objectives.

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