Convergence and Accuracy Trade-Offs in Federated Learning and Meta-Learning

Zachary Charles, Jakub Konečný
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:2575-2583, 2021.

Abstract

We study a family of algorithms, which we refer to as local update methods, generalizing many federated and meta-learning algorithms. We prove that for quadratic models, local update methods are equivalent to first-order optimization on a surrogate loss we exactly characterize. Moreover, fundamental algorithmic choices (such as learning rates) explicitly govern a trade-off between the condition number of the surrogate loss and its alignment with the true loss. We derive novel convergence rates showcasing these trade-offs and highlight their importance in communication-limited settings. Using these insights, we are able to compare local update methods based on their convergence/accuracy trade-off, not just their convergence to critical points of the empirical loss. Our results shed new light on a broad range of phenomena, including the efficacy of server momentum in federated learning and the impact of proximal client updates.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-charles21a, title = { Convergence and Accuracy Trade-Offs in Federated Learning and Meta-Learning }, author = {Charles, Zachary and Kone\v{c}n\'y, Jakub}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {2575--2583}, 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/charles21a/charles21a.pdf}, url = {https://proceedings.mlr.press/v130/charles21a.html}, abstract = { We study a family of algorithms, which we refer to as local update methods, generalizing many federated and meta-learning algorithms. We prove that for quadratic models, local update methods are equivalent to first-order optimization on a surrogate loss we exactly characterize. Moreover, fundamental algorithmic choices (such as learning rates) explicitly govern a trade-off between the condition number of the surrogate loss and its alignment with the true loss. We derive novel convergence rates showcasing these trade-offs and highlight their importance in communication-limited settings. Using these insights, we are able to compare local update methods based on their convergence/accuracy trade-off, not just their convergence to critical points of the empirical loss. Our results shed new light on a broad range of phenomena, including the efficacy of server momentum in federated learning and the impact of proximal client updates. } }
Endnote
%0 Conference Paper %T Convergence and Accuracy Trade-Offs in Federated Learning and Meta-Learning %A Zachary Charles %A Jakub Konečný %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-charles21a %I PMLR %P 2575--2583 %U https://proceedings.mlr.press/v130/charles21a.html %V 130 %X We study a family of algorithms, which we refer to as local update methods, generalizing many federated and meta-learning algorithms. We prove that for quadratic models, local update methods are equivalent to first-order optimization on a surrogate loss we exactly characterize. Moreover, fundamental algorithmic choices (such as learning rates) explicitly govern a trade-off between the condition number of the surrogate loss and its alignment with the true loss. We derive novel convergence rates showcasing these trade-offs and highlight their importance in communication-limited settings. Using these insights, we are able to compare local update methods based on their convergence/accuracy trade-off, not just their convergence to critical points of the empirical loss. Our results shed new light on a broad range of phenomena, including the efficacy of server momentum in federated learning and the impact of proximal client updates.
APA
Charles, Z. & Konečný, J.. (2021). Convergence and Accuracy Trade-Offs in Federated Learning and Meta-Learning . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:2575-2583 Available from https://proceedings.mlr.press/v130/charles21a.html.

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