Abstract: Multi-agent machine learning has seen tremendous achievements in recent years; yet, translation of single-agent optimization technique to multi-agent domain may not be straightforward. Two of the basic models for multi-agent machine learning -- minimax optimization problem and variational inequality problem -- are both computationally intractable in general. However, the gains from leveraging the special structures can be huge and understanding the optimal structure-driven algorithm is important from both theoretical and practical viewpoints. In this talk, I will provide the results on the optimal structure-driven algorithm design for (1) convex-concave and highly unbalanced minimax optimization problems and (2) monotone and highly smooth variational inequality problems. In particular, I explain why the accelerated proximal point scheme and the adaptive closed-loop scheme perfectly fit the unbalanced structure and the highly smooth structure, respectively, leading to optimal acceleration in our problem of interest.