CSE DSI Machine Learning Seminar with Yulong Lu (Math, UMN)

Two-scale gradient descent ascent dynamics finds mixed Nash equilibria of continuous games: A mean-field perspective

Finding the mixed Nash equilibria (MNE) of a two-player zero sum continuous game is an important and challenging problem in machine learning. A canonical algorithm to finding the MNE is the (noisy) gradient descent ascent (GDA) method. In this talk, we will discuss the infinite particle limit of the GDA dynamics and its convergence properties. Specifically, we show that for each finite temperature (or regularization parameter), the two-scale Mean-Field GDA with a suitable {\em finite} scale ratio converges exponentially to the unique MNE without assuming the convexity or concavity of the interaction potential. We further study the simulated annealing of the Mean-Field GDA dynamics. We show that with a temperature schedule that decays logarithmically in time the annealed Mean-Field GDA converges to the MNE of the original unregularized objective.

Dr. Yulong Lu is an Assistant Professor in the School of Mathematics at University of Minnesota Twin Cities. His research interests include applied analysis, applied probability and statistics. His recent research interests are focused on the mathematical foundation of machine learning with applications in PDEs and inverse problems.