SILVER: Single-loop variance reduction and application to federated learning

Kazusato Oko, Shunta Akiyama, Denny Wu, Tomoya Murata, Taiji Suzuki
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:38683-38739, 2024.

Abstract

Most variance reduction methods require multiple times of full gradient computation, which is time-consuming and hence a bottleneck in application to distributed optimization. We present a single-loop variance-reduced gradient estimator named SILVER (SIngle-Loop VariancE-Reduction) for the finite-sum non-convex optimization, which does not require multiple full gradients but nevertheless achieves the optimal gradient complexity. Notably, unlike existing methods, SILVER provably reaches second-order optimality, with exponential convergence in the Polyak-Łojasiewicz (PL) region, and achieves further speedup depending on the data heterogeneity. Owing to these advantages, SILVER serves as a new base method to design communication-efficient federated learning algorithms: we combine SILVER with local updates which gives the best communication rounds and number of communicated gradients across all range of Hessian heterogeneity, and, at the same time, guarantees second-order optimality and exponential convergence in the PL region.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-oko24a, title = {{SILVER}: Single-loop variance reduction and application to federated learning}, author = {Oko, Kazusato and Akiyama, Shunta and Wu, Denny and Murata, Tomoya and Suzuki, Taiji}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {38683--38739}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/oko24a/oko24a.pdf}, url = {https://proceedings.mlr.press/v235/oko24a.html}, abstract = {Most variance reduction methods require multiple times of full gradient computation, which is time-consuming and hence a bottleneck in application to distributed optimization. We present a single-loop variance-reduced gradient estimator named SILVER (SIngle-Loop VariancE-Reduction) for the finite-sum non-convex optimization, which does not require multiple full gradients but nevertheless achieves the optimal gradient complexity. Notably, unlike existing methods, SILVER provably reaches second-order optimality, with exponential convergence in the Polyak-Łojasiewicz (PL) region, and achieves further speedup depending on the data heterogeneity. Owing to these advantages, SILVER serves as a new base method to design communication-efficient federated learning algorithms: we combine SILVER with local updates which gives the best communication rounds and number of communicated gradients across all range of Hessian heterogeneity, and, at the same time, guarantees second-order optimality and exponential convergence in the PL region.} }
Endnote
%0 Conference Paper %T SILVER: Single-loop variance reduction and application to federated learning %A Kazusato Oko %A Shunta Akiyama %A Denny Wu %A Tomoya Murata %A Taiji Suzuki %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-oko24a %I PMLR %P 38683--38739 %U https://proceedings.mlr.press/v235/oko24a.html %V 235 %X Most variance reduction methods require multiple times of full gradient computation, which is time-consuming and hence a bottleneck in application to distributed optimization. We present a single-loop variance-reduced gradient estimator named SILVER (SIngle-Loop VariancE-Reduction) for the finite-sum non-convex optimization, which does not require multiple full gradients but nevertheless achieves the optimal gradient complexity. Notably, unlike existing methods, SILVER provably reaches second-order optimality, with exponential convergence in the Polyak-Łojasiewicz (PL) region, and achieves further speedup depending on the data heterogeneity. Owing to these advantages, SILVER serves as a new base method to design communication-efficient federated learning algorithms: we combine SILVER with local updates which gives the best communication rounds and number of communicated gradients across all range of Hessian heterogeneity, and, at the same time, guarantees second-order optimality and exponential convergence in the PL region.
APA
Oko, K., Akiyama, S., Wu, D., Murata, T. & Suzuki, T.. (2024). SILVER: Single-loop variance reduction and application to federated learning. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:38683-38739 Available from https://proceedings.mlr.press/v235/oko24a.html.

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