# Local Steps Speed Up Local GD for Heterogeneous Distributed Logistic Regression

arXiv: https://arxiv.org/abs/2501.13790 · HTML: https://mlsanity.com/paper/2501.13790/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2025.

## Built on by (most cited first, 2 of 2)

- [Constant Stepsize Local GD for Logistic Regression: Acceleration by Instability](https://mlsanity.com/paper/2506.13974/) (2025)
- [Tight Bounds for Logistic Regression with Large Stepsize Gradient Descent in Low Dimension](https://mlsanity.com/paper/2602.12471/) (2026)

## Abstract (arXiv)

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 Omega(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 gg 1/K, whereas prior analysis depends on η ≤ 1/K.