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# Accelerated Algorithms for Smooth Convex-Concave Minimax Problems with O(1/k^2) Rate on Squared Gradient Norm

*Proceedings of the 38th International Conference on Machine Learning*, PMLR 139:12098-12109, 2021.

#### 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.