Local SGD: Unified Theory and New Efficient Methods
Eduard Gorbunov, Filip Hanzely, Peter Richtarik
Abstract
We present a unified framework for analyzing local SGD methods in the convex and strongly convex regimes for distributed/federated training of supervised machine learning models. We recover several known methods as a special case of our general framework, including Local SGD/FedAvg, SCAFFOLD, and several variants of SGD not originally designed for federated learning. Our framework covers both the identical and heterogeneous data settings, supports both random and deterministic number of local steps, and can work with a wide array of local stochastic gradient estimators, including shifted estimators which are able to adjust the fixed points of local iterations for faster convergence. As an application of our framework, we develop multiple novel FL optimizers which are superior to existing methods. In particular, we develop the first linearly converging local SGD method which does not require any data homogeneity or other strong assumptions.
BibTeX
@InProceedings{pmlr-v130-gorbunov21a,
title = { Local SGD: Unified Theory and New Efficient Methods },
author = {Gorbunov, Eduard and Hanzely, Filip and Richtarik, Peter},
booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
pages = {3556--3564},
year = {2021},
editor = {Banerjee, Arindam and Fukumizu, Kenji},
volume = {130},
series = {Proceedings of Machine Learning Research},
month = {13--15 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v130/gorbunov21a/gorbunov21a.pdf},
url = {https://proceedings.mlr.press/v130/gorbunov21a.html},
abstract = { We present a unified framework for analyzing local SGD methods in the convex and strongly convex regimes for distributed/federated training of supervised machine learning models. We recover several known methods as a special case of our general framework, including Local SGD/FedAvg, SCAFFOLD, and several variants of SGD not originally designed for federated learning. Our framework covers both the identical and heterogeneous data settings, supports both random and deterministic number of local steps, and can work with a wide array of local stochastic gradient estimators, including shifted estimators which are able to adjust the fixed points of local iterations for faster convergence. As an application of our framework, we develop multiple novel FL optimizers which are superior to existing methods. In particular, we develop the first linearly converging local SGD method which does not require any data homogeneity or other strong assumptions. }
}