Avoid Overclaims: Summary of Complexity Bounds for Algorithms in Minimization and Minimax Optimization

In this blog, we summarize the upper and lower complexity bounds of first-order algorithms in minimization and minimax optimization problems. Within the classical oracle model framework, we review the state-of-the-art upper and lower bound results in various settings, aiming to identify gaps in existing research. With the rapid development of applications like machine learning and operation research, we further identify some recent works that revised the classical settings of optimization algorithms study.