The goal of this project is to characterize the convergence of two-player optimization dynamics. Our initial investigation is into convex-concave (saddle point) functions, where we investigate the convergence of the optimistic mirror descent algorithm. When this result is explained, we can continue to investigate general properties of optimization dynamics in potentially multidimensional games. Specifically, the project is inspired from earlier papers that characterize the optimization dynamics in terms of average-convergence to equilibria in two-player table games. In our research, we hope to extend these works to show final-step convergence, as well as extend beyond table games into the realm of general convex-concave functions.

In doing this SuperUROP project, I hope to apply the mathematics and computer science I’ve learned in classes such as Inference and Information (6.437) and (Topics in Algorithmic Game Theory (6.853) to explore and develop new methods and results. I’m excited to dive into deep theoretical work with many interesting applications!