# Local SGD Converges Fast and Communicates Little

Source: [Local SGD Converges Fast and Communicates Little](<https://www.sota2.com/research/paper/68fa55cd1e209131ce9976e7>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T13:48:43.673Z

Authors: Sebastian U. Stich

Published: 2018-05-24T16:38:51.000Z

## Abstract

Mini-batch stochastic gradient descent (SGD) is state of the art in large scale distributed training. The scheme can reach a linear speedup with respect to the number of workers, but this is rarely seen in practice as the scheme often suffers from large network delays and bandwidth limits. To overcome this communication bottleneck recent works propose to reduce the communication frequency. An algorithm of this type is local SGD that runs SGD independently in parallel on different workers and averages the sequences only once in a while.   This scheme shows promising results in practice, but eluded thorough theoretical analysis. We prove concise convergence rates for local SGD on convex problems and show that it converges at the same rate as mini-batch SGD in terms of number of evaluated gradients, that is, the scheme achieves linear speedup in the number of workers and mini-batch size. The number of communication rounds can be reduced up to a factor of T^{1/2}---where T denotes the number of total steps---compared to mini-batch SGD. This also holds for asynchronous implementations. Local SGD can also be used for large scale training of deep learning models.   The results shown here aim serving as a guideline to further explore the theoretical and practical aspects of local SGD in these applications.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Classification on CIFAR-100 (test) (Error Rate and Communication Overhead)](<https://www.sota2.com/research/sota/image-classification-on-cifar-100-test-error-rate-and-communication-overhead.md>): Image Classification; CIFAR-100 (test); Test Error Rate: 18.82.

- [Image Classification on CIFAR-10 (test) (Error Rate and Communication Cost)](<https://www.sota2.com/research/sota/image-classification-on-cifar-10-test-error-rate-and-communication-cost.md>): Image Classification; CIFAR-10 (test); Test Error Rate: 4.36.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1805.09767>)

[PDF](<https://arxiv.org/pdf/1805.09767.pdf>)