The Geometry of Fast Last-Iterate Learning in Games

Learning in games involves the study of online learning algorithms in strategic, multi-agent settings. Here, a central question is to understand which structural properties of games and which properties of algorithms together drive fast last-iterate convergence to a Nash equilibrium.

 

In this talk, we present a geometric perspective for studying this question for a canonical family of regularized learning dynamics. By analyzing the trajectories of these dynamics in a dual space, we gain a more intuitive, physics-inspired characterization of when and why their iterates converge to equilibrium in the primal space. We use this perspective to establish a variety of new and optimal quantitative guarantees in both two-player zero-sum games and in multiplayer harmonic games. We conclude by discussing several open directions.