Delving into the Convergence of Generalized Smooth Minimax Optimization

Wenhan Xian, Ziyi Chen, Heng Huang
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:54191-54211, 2024.

Abstract

Minimax optimization is fundamental and important for enormous machine learning applications such as generative adversarial network, adversarial training, and robust optimization. Recently, a variety of minimax algorithms with theoretical guarantees based on Lipschitz smoothness have been proposed. However, these algorithms could fail to converge in practice because the requisite Lipschitz smooth condition may not hold even in some classic minimax problems. We will present some counterexamples to reveal this divergence issue. Thus, to fill this gap, we are motivated to delve into the convergence analysis of minimax algorithms under a relaxed Lipschitz smoothness condition, i.e., generalized smoothness. We prove that variants of basic minimax optimization algorithms GDA, SGDA, GDmax and SGDmax can still converge in generalized smooth problems, and hence their theoretical guarantees can be extended to a wider range of applications. We also conduct a numerical experiment to validate the performance of our proposed algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-xian24a, title = {Delving into the Convergence of Generalized Smooth Minimax Optimization}, author = {Xian, Wenhan and Chen, Ziyi and Huang, Heng}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {54191--54211}, 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/xian24a/xian24a.pdf}, url = {https://proceedings.mlr.press/v235/xian24a.html}, abstract = {Minimax optimization is fundamental and important for enormous machine learning applications such as generative adversarial network, adversarial training, and robust optimization. Recently, a variety of minimax algorithms with theoretical guarantees based on Lipschitz smoothness have been proposed. However, these algorithms could fail to converge in practice because the requisite Lipschitz smooth condition may not hold even in some classic minimax problems. We will present some counterexamples to reveal this divergence issue. Thus, to fill this gap, we are motivated to delve into the convergence analysis of minimax algorithms under a relaxed Lipschitz smoothness condition, i.e., generalized smoothness. We prove that variants of basic minimax optimization algorithms GDA, SGDA, GDmax and SGDmax can still converge in generalized smooth problems, and hence their theoretical guarantees can be extended to a wider range of applications. We also conduct a numerical experiment to validate the performance of our proposed algorithms.} }
Endnote
%0 Conference Paper %T Delving into the Convergence of Generalized Smooth Minimax Optimization %A Wenhan Xian %A Ziyi Chen %A Heng Huang %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-xian24a %I PMLR %P 54191--54211 %U https://proceedings.mlr.press/v235/xian24a.html %V 235 %X Minimax optimization is fundamental and important for enormous machine learning applications such as generative adversarial network, adversarial training, and robust optimization. Recently, a variety of minimax algorithms with theoretical guarantees based on Lipschitz smoothness have been proposed. However, these algorithms could fail to converge in practice because the requisite Lipschitz smooth condition may not hold even in some classic minimax problems. We will present some counterexamples to reveal this divergence issue. Thus, to fill this gap, we are motivated to delve into the convergence analysis of minimax algorithms under a relaxed Lipschitz smoothness condition, i.e., generalized smoothness. We prove that variants of basic minimax optimization algorithms GDA, SGDA, GDmax and SGDmax can still converge in generalized smooth problems, and hence their theoretical guarantees can be extended to a wider range of applications. We also conduct a numerical experiment to validate the performance of our proposed algorithms.
APA
Xian, W., Chen, Z. & Huang, H.. (2024). Delving into the Convergence of Generalized Smooth Minimax Optimization. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:54191-54211 Available from https://proceedings.mlr.press/v235/xian24a.html.

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