The First Optimal Algorithm for Smooth and Strongly-Convex-Strongly-Concave Minimax Optimization. (arXiv:2205.05653v1 [math.OC])

In this paper, we revisit the smooth and strongly-convex-strongly-concave
minimax optimization problem. Zhang et al. (2021) and Ibrahim et al. (2020)
established the lower bound $\Omega\left(\sqrt{\kappa_x\kappa_y} \log
\frac{1}{\epsilon}\right)$ on the number of gradient evaluations required to
find an $\epsilon$-accurate solution, where $\kappa_x$ and $\kappa_y$ are
condition numbers for the strong convexity and strong concavity assumptions.
However, the existing state-of-the-art methods do not match this lower bound:
algorithms of Lin et al. (2020) and Wang and Li (2020) have gradient evaluation …

algorithm arxiv math minimax optimization