We analyze two variants of Local Gradient Descent applied to distributed logistic regression with heterogeneous, separable data and show convergence at the rate O(1/KR) for K local steps and sufficiently large R communication rounds. In contrast, all existing convergence guarantees for Local GD applied to any problem are at least Ω(1/R), meaning they fail to show the benefit of local updates. The key to our improved guarantee is showing progress on the logistic regression objective when using a large stepsize η≫1/K, whereas prior analysis depends on η≤1/K.
@article{arxiv.2501.13790,
title = {Local Steps Speed Up Local GD for Heterogeneous Distributed Logistic Regression},
author = {Michael Crawshaw and Blake Woodworth and Mingrui Liu},
journal= {arXiv preprint arXiv:2501.13790},
year = {2025}
}