Achieving Linear Speedup in Non-IID Federated Bilevel Learning

Minhui Huang, Dewei Zhang, Kaiyi Ji
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:14039-14059, 2023.

Abstract

Federated bilevel learning has received increasing attention in various emerging machine learning and communication applications. Recently, several Hessian-vector-based algorithms have been proposed to solve the federated bilevel optimization problem. However, several important properties in federated learning such as the partial client participation and the linear speedup for convergence (i.e., the convergence rate and complexity are improved linearly with respect to the number of sampled clients) in the presence of non-i.i.d. datasets, still remain open. In this paper, we fill these gaps by proposing a new federated bilevel algorithm named FedMBO with a novel client sampling scheme in the federated hypergradient estimation. We show that FedMBO achieves a convergence rate of $\mathcal{O}\big(\frac{1}{\sqrt{nK}}+\frac{1}{K}+\frac{\sqrt{n}}{K^{3/2}}\big)$ on non-i.i.d. datasets, where $n$ is the number of participating clients in each round, and $K$ is the total number of iteration. This is the first theoretical linear speedup result for non-i.i.d. federated bilevel optimization. Extensive experiments validate our theoretical results and demonstrate the effectiveness of our proposed method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-huang23p, title = {Achieving Linear Speedup in Non-{IID} Federated Bilevel Learning}, author = {Huang, Minhui and Zhang, Dewei and Ji, Kaiyi}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {14039--14059}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/huang23p/huang23p.pdf}, url = {https://proceedings.mlr.press/v202/huang23p.html}, abstract = {Federated bilevel learning has received increasing attention in various emerging machine learning and communication applications. Recently, several Hessian-vector-based algorithms have been proposed to solve the federated bilevel optimization problem. However, several important properties in federated learning such as the partial client participation and the linear speedup for convergence (i.e., the convergence rate and complexity are improved linearly with respect to the number of sampled clients) in the presence of non-i.i.d. datasets, still remain open. In this paper, we fill these gaps by proposing a new federated bilevel algorithm named FedMBO with a novel client sampling scheme in the federated hypergradient estimation. We show that FedMBO achieves a convergence rate of $\mathcal{O}\big(\frac{1}{\sqrt{nK}}+\frac{1}{K}+\frac{\sqrt{n}}{K^{3/2}}\big)$ on non-i.i.d. datasets, where $n$ is the number of participating clients in each round, and $K$ is the total number of iteration. This is the first theoretical linear speedup result for non-i.i.d. federated bilevel optimization. Extensive experiments validate our theoretical results and demonstrate the effectiveness of our proposed method.} }
Endnote
%0 Conference Paper %T Achieving Linear Speedup in Non-IID Federated Bilevel Learning %A Minhui Huang %A Dewei Zhang %A Kaiyi Ji %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-huang23p %I PMLR %P 14039--14059 %U https://proceedings.mlr.press/v202/huang23p.html %V 202 %X Federated bilevel learning has received increasing attention in various emerging machine learning and communication applications. Recently, several Hessian-vector-based algorithms have been proposed to solve the federated bilevel optimization problem. However, several important properties in federated learning such as the partial client participation and the linear speedup for convergence (i.e., the convergence rate and complexity are improved linearly with respect to the number of sampled clients) in the presence of non-i.i.d. datasets, still remain open. In this paper, we fill these gaps by proposing a new federated bilevel algorithm named FedMBO with a novel client sampling scheme in the federated hypergradient estimation. We show that FedMBO achieves a convergence rate of $\mathcal{O}\big(\frac{1}{\sqrt{nK}}+\frac{1}{K}+\frac{\sqrt{n}}{K^{3/2}}\big)$ on non-i.i.d. datasets, where $n$ is the number of participating clients in each round, and $K$ is the total number of iteration. This is the first theoretical linear speedup result for non-i.i.d. federated bilevel optimization. Extensive experiments validate our theoretical results and demonstrate the effectiveness of our proposed method.
APA
Huang, M., Zhang, D. & Ji, K.. (2023). Achieving Linear Speedup in Non-IID Federated Bilevel Learning. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:14039-14059 Available from https://proceedings.mlr.press/v202/huang23p.html.

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