Equilibrium Computation, Deep Learning, and Multi-Agent Reinforcement Learning (Invited Talk)

Machine Learning has recently made significant advances in challenges such as speech and image recognition, automatic translation, and text generation, much of that progress being fueled by the success of gradient descent-based optimization methods in computing local optima of non-convex objectives. From robustifying machine learning models against adversarial attacks to causal inference, training generative models, multi-robot interactions, and learning in strategic environments, many outstanding challenges in Machine Learning lie at its interface with Game Theory. On this front, however, gradient-descent based optimization methods have been less successful. Here, the role of single-objective optimization is played by equilibrium computation, but gradient-descent based methods commonly fail to find equilibria, and even computing local approximate equilibria has remained daunting. We shed light on these challenges through a combination of learning-theoretic, complexity-theoretic, game-theoretic and topological techniques, presenting obstacles and opportunities for Machine Learning and Game Theory going forward. I will assume no Deep Learning background for this talk and present results from joint works with S. Skoulakis and M. Zampetakis [Daskalakis et al., 2021] as well as with N. Golowich and K. Zhang [Daskalakis et al., 2022]