ICML 2021oral137 citations
Accelerated Algorithms for Smooth Convex-Concave Minimax Problems with O(1/k^2) Rate on Squared Gradient Norm
Abstract
In this work, we study the computational complexity of reducing the squared gradient magnitude for smooth minimax optimization problems. First, we present algorithms with accelerated $\mathcal{O}(1/k^2)$ last-iterate rates, faster than the existing $\mathcal{O}(1/k)$ or slower rates for extragradient, Popov, and gradient descent with anchoring. The acceleration mechanism combines extragradient steps with anchoring and is distinct from Nesterov’s acceleration. We then establish optimality of the $\mathcal{O}(1/k^2)$ rate through a matching lower bound.
BibTeX
@InProceedings{pmlr-v139-yoon21d,
title = {Accelerated Algorithms for Smooth Convex-Concave Minimax Problems with O(1/k^2) Rate on Squared Gradient Norm},
author = {Yoon, Taeho and Ryu, Ernest K},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {12098--12109},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/yoon21d/yoon21d.pdf},
url = {https://proceedings.mlr.press/v139/yoon21d.html},
abstract = {In this work, we study the computational complexity of reducing the squared gradient magnitude for smooth minimax optimization problems. First, we present algorithms with accelerated $\mathcal{O}(1/k^2)$ last-iterate rates, faster than the existing $\mathcal{O}(1/k)$ or slower rates for extragradient, Popov, and gradient descent with anchoring. The acceleration mechanism combines extragradient steps with anchoring and is distinct from Nesterov’s acceleration. We then establish optimality of the $\mathcal{O}(1/k^2)$ rate through a matching lower bound.}
}