Multiplicative Weight Update

Multiplicative Weight Update (MWU) methods are iterative algorithms used to solve optimization problems, particularly in game theory and online learning, aiming to find optimal strategies or equilibria. Current research focuses on improving the convergence rates of MWU and its variants, such as Optimistic MWU (OMWU), especially concerning last-iterate convergence and addressing challenges in settings with noisy feedback or infinite strategy spaces, as seen in quantum games. These advancements have significant implications for various fields, including machine learning (e.g., fair classification), and provide efficient algorithms for solving large-scale games and optimization problems with complex constraints.