Error Feedback Fixes SignSGD and other Gradient Compression Schemes
Sai Praneeth Karimireddy, Quentin Rebjock, Sebastian Stich, Martin Jaggi
Abstract
Sign-based algorithms (e.g. signSGD) have been proposed as a biased gradient compression technique to alleviate the communication bottleneck in training large neural networks across multiple workers. We show simple convex counter-examples where signSGD does not converge to the optimum. Further, even when it does converge, signSGD may generalize poorly when compared with SGD. These issues arise because of the biased nature of the sign compression operator. We then show that using error-feedback, i.e. incorporating the error made by the compression operator into the next step, overcomes these issues. We prove that our algorithm (EF-SGD) with arbitrary compression operator achieves the same rate of convergence as SGD without any additional assumptions. Thus EF-SGD achieves gradient compression for free. Our experiments thoroughly substantiate the theory.
BibTeX
@InProceedings{pmlr-v97-karimireddy19a,
title = {Error Feedback Fixes {S}ign{SGD} and other Gradient Compression Schemes},
author = {Karimireddy, Sai Praneeth and Rebjock, Quentin and Stich, Sebastian and Jaggi, Martin},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {3252--3261},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/karimireddy19a/karimireddy19a.pdf},
url = {https://proceedings.mlr.press/v97/karimireddy19a.html},
abstract = {Sign-based algorithms (e.g. signSGD) have been proposed as a biased gradient compression technique to alleviate the communication bottleneck in training large neural networks across multiple workers. We show simple convex counter-examples where signSGD does not converge to the optimum. Further, even when it does converge, signSGD may generalize poorly when compared with SGD. These issues arise because of the biased nature of the sign compression operator. We then show that using error-feedback, i.e. incorporating the error made by the compression operator into the next step, overcomes these issues. We prove that our algorithm (EF-SGD) with arbitrary compression operator achieves the same rate of convergence as SGD without any additional assumptions. Thus EF-SGD achieves gradient compression for free. Our experiments thoroughly substantiate the theory.}
}