Title: What Can Optimization Theory Offer to Equilibrium Computation?

Abstract: In this talk, I will first give a brief overview of optimization theory from an algorithmic point of view and position the contribution of our works properly. More specifically, I focus on new problems pertaining to equilibrium computation: nonconvex-concave min-max optimization problems and generalized Nash equilibrium problems. To design the efficient first-order numerical schemes with nonasymptotic theoretical guarantee, we investigate their special structures and give the reasonable optimality condition as well as simple and intuitive numerical schemes. In summary, our works are typical examples in developing new algorithms for equilibrium computation via appeal to basic principles in this history and we hope that our perspective may be useful more broadly.

Bio: Tianyi Lin is a PhD student in EECS at UC Berkeley where he is advised by Michael. I. Jordan. Before Berkeley, he received a BA in Mathematics from Nanjing University and a MASt in Mathematics from University of Cambridge. His research interests include algorithmic design and applications to machine learning, especially the multi-agent learning in games and optimal transport.

List of related papers:

1. On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems. (https://arxiv.org/abs/1906.00331)
2. First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problems. (https://arxiv.org/abs/2204.03132)