Federated Learning with Compression: Unified Analysis and Sharp Guarantees
Farzin Haddadpour, Mohammad Mahdi Kamani, Aryan Mokhtari, Mehrdad Mahdavi
Abstract
In federated learning, communication cost is often a critical bottleneck to scale up distributed optimization algorithms to collaboratively learn a model from millions of devices with potentially unreliable or limited communication and heterogeneous data distributions. Two notable trends to deal with the communication overhead of federated algorithms are gradient compression and local computation with periodic communication. Despite many attempts, characterizing the relationship between these two approaches has proven elusive. We address this by proposing a set of algorithms with periodical compressed (quantized or sparsified) communication and analyze their convergence properties in both homogeneous and heterogeneous local data distributions settings. For the homogeneous setting, our analysis improves existing bounds by providing tighter convergence rates for both strongly convex and non-convex objective functions. To mitigate data heterogeneity, we introduce a local gradient tracking scheme and obtain sharp convergence rates that match the best-known communication complexities without compression for convex, strongly convex, and nonconvex settings. We complement our theoretical results by demonstrating the effectiveness of our proposed methods on real-world datasets.
BibTeX
@InProceedings{pmlr-v130-haddadpour21a,
title = { Federated Learning with Compression: Unified Analysis and Sharp Guarantees },
author = {Haddadpour, Farzin and Kamani, Mohammad Mahdi and Mokhtari, Aryan and Mahdavi, Mehrdad},
booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
pages = {2350--2358},
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/haddadpour21a/haddadpour21a.pdf},
url = {https://proceedings.mlr.press/v130/haddadpour21a.html},
abstract = { In federated learning, communication cost is often a critical bottleneck to scale up distributed optimization algorithms to collaboratively learn a model from millions of devices with potentially unreliable or limited communication and heterogeneous data distributions. Two notable trends to deal with the communication overhead of federated algorithms are gradient compression and local computation with periodic communication. Despite many attempts, characterizing the relationship between these two approaches has proven elusive. We address this by proposing a set of algorithms with periodical compressed (quantized or sparsified) communication and analyze their convergence properties in both homogeneous and heterogeneous local data distributions settings. For the homogeneous setting, our analysis improves existing bounds by providing tighter convergence rates for both strongly convex and non-convex objective functions. To mitigate data heterogeneity, we introduce a local gradient tracking scheme and obtain sharp convergence rates that match the best-known communication complexities without compression for convex, strongly convex, and nonconvex settings. We complement our theoretical results by demonstrating the effectiveness of our proposed methods on real-world datasets. }
}