Lecture
This lecture explores the behavior of learning dynamics in zero-sum and congestion games, drawing parallels with conservative systems. It delves into no-regret algorithms, such as Follow the Regularized Leader, and their convergence to Nash equilibria. The instructor discusses the implications of Poincaré recurrence in game dynamics and the concept of limit cycles. Chaos and butterfly effects in Follow-the-Regularized Leader dynamics are also examined, highlighting the interplay between chaos and local stability. The session concludes with insights on the emergence of chaos in online learning dynamics, showcasing the intricate relationship between time-average convergence and chaos.