Federated Minimax Optimization: Improved Convergence Analyses and Algorithms

Pranay Sharma, Rohan Panda, Gauri Joshi, Pramod Varshney
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:19683-19730, 2022.

Abstract

In this paper, we consider nonconvex minimax optimization, which is gaining prominence in many modern machine learning applications, such as GANs. Large-scale edge-based collection of training data in these applications calls for communication-efficient distributed optimization algorithms, such as those used in federated learning, to process the data. In this paper, we analyze local stochastic gradient descent ascent (SGDA), the local-update version of the SGDA algorithm. SGDA is the core algorithm used in minimax optimization, but it is not well-understood in a distributed setting. We prove that Local SGDA has order-optimal sample complexity for several classes of nonconvex-concave and nonconvex-nonconcave minimax problems, and also enjoys linear speedup with respect to the number of clients. We provide a novel and tighter analysis, which improves the convergence and communication guarantees in the existing literature. For nonconvex-PL and nonconvex-one-point-concave functions, we improve the existing complexity results for centralized minimax problems. Furthermore, we propose a momentum-based local-update algorithm, which has the same convergence guarantees, but outperforms Local SGDA as demonstrated in our experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-sharma22c, title = {Federated Minimax Optimization: Improved Convergence Analyses and Algorithms}, author = {Sharma, Pranay and Panda, Rohan and Joshi, Gauri and Varshney, Pramod}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {19683--19730}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/sharma22c/sharma22c.pdf}, url = {https://proceedings.mlr.press/v162/sharma22c.html}, abstract = {In this paper, we consider nonconvex minimax optimization, which is gaining prominence in many modern machine learning applications, such as GANs. Large-scale edge-based collection of training data in these applications calls for communication-efficient distributed optimization algorithms, such as those used in federated learning, to process the data. In this paper, we analyze local stochastic gradient descent ascent (SGDA), the local-update version of the SGDA algorithm. SGDA is the core algorithm used in minimax optimization, but it is not well-understood in a distributed setting. We prove that Local SGDA has order-optimal sample complexity for several classes of nonconvex-concave and nonconvex-nonconcave minimax problems, and also enjoys linear speedup with respect to the number of clients. We provide a novel and tighter analysis, which improves the convergence and communication guarantees in the existing literature. For nonconvex-PL and nonconvex-one-point-concave functions, we improve the existing complexity results for centralized minimax problems. Furthermore, we propose a momentum-based local-update algorithm, which has the same convergence guarantees, but outperforms Local SGDA as demonstrated in our experiments.} }
Endnote
%0 Conference Paper %T Federated Minimax Optimization: Improved Convergence Analyses and Algorithms %A Pranay Sharma %A Rohan Panda %A Gauri Joshi %A Pramod Varshney %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-sharma22c %I PMLR %P 19683--19730 %U https://proceedings.mlr.press/v162/sharma22c.html %V 162 %X In this paper, we consider nonconvex minimax optimization, which is gaining prominence in many modern machine learning applications, such as GANs. Large-scale edge-based collection of training data in these applications calls for communication-efficient distributed optimization algorithms, such as those used in federated learning, to process the data. In this paper, we analyze local stochastic gradient descent ascent (SGDA), the local-update version of the SGDA algorithm. SGDA is the core algorithm used in minimax optimization, but it is not well-understood in a distributed setting. We prove that Local SGDA has order-optimal sample complexity for several classes of nonconvex-concave and nonconvex-nonconcave minimax problems, and also enjoys linear speedup with respect to the number of clients. We provide a novel and tighter analysis, which improves the convergence and communication guarantees in the existing literature. For nonconvex-PL and nonconvex-one-point-concave functions, we improve the existing complexity results for centralized minimax problems. Furthermore, we propose a momentum-based local-update algorithm, which has the same convergence guarantees, but outperforms Local SGDA as demonstrated in our experiments.
APA
Sharma, P., Panda, R., Joshi, G. & Varshney, P.. (2022). Federated Minimax Optimization: Improved Convergence Analyses and Algorithms. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:19683-19730 Available from https://proceedings.mlr.press/v162/sharma22c.html.

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