Variance Reduced Local SGD with Lower Communication Complexity

Xianfeng Liang, Shuheng Shen, Jingchang Liu, Zhen Pan, Yifei Cheng, Enhong Chen

Keywords: variance reduction, local SGD, distributed optimization

TL;DR: We prove that the proposed algorithm can achieve linear iteration speedup with lower communication complexity than Local SGD and the experimental results verify our theoretical clarification.

Abstract: To accelerate the training of machine learning models, distributed stochastic gradient descent (SGD) and its variants have been widely adopted, which apply multiple workers in parallel to speed up training. Among them, Local SGD has gained much attention due to its lower communication cost. Nevertheless, when the data distribution on workers is non-identical, Local SGD requires $O(T^{\frac{3}{4}} N^{\frac{3}{4}})$ communications to maintain its \emph{linear iteration speedup} property, where $T$ is the total number of iterations and $N$ is the number of workers. In this paper, we propose Variance Reduced Local SGD (VRL-SGD) to further reduce the communication complexity. Benefiting from eliminating the dependency on the gradient variance among workers, we theoretically prove that VRL-SGD achieves a \emph{linear iteration speedup} with a lower communication complexity $O(T^{\frac{1}{2}} N^{\frac{3}{2}})$ even if workers access non-identical datasets. We conduct experiments on three machine learning tasks, and the experimental results demonstrate that VRL-SGD performs impressively better than Local SGD when the data among workers are quite diverse.

Code: https://github.com/VRL-SGD/VRL-SGD

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:1912.12844/code)