Global Convergence Guarantee

Global convergence guarantees in optimization aim to ensure algorithms reliably find the optimal solution, a crucial challenge in non-convex problems prevalent in machine learning. Current research focuses on establishing such guarantees for various algorithms, including policy gradient methods in reinforcement learning, federated learning schemes, and optimal transport solvers, often employing techniques like dynamical low-rank approximations or entropic regularization. These advancements improve the reliability and efficiency of training complex models, impacting fields like computer vision, multi-agent systems, and control systems by providing more robust and predictable performance.