Fundamental Lemma

The "fundamental lemma" encompasses a family of mathematical results used to establish convergence rates in various fields, from optimization algorithms to reinforcement learning. Current research focuses on tightening existing bounds, generalizing lemmas to broader classes of problems (e.g., non-convex optimization, nonlinear systems), and exploring connections between different fundamental lemmas and related techniques like kernel regression. These advancements improve the theoretical understanding and practical performance of numerous algorithms across machine learning, optimization, and other areas, leading to more efficient and robust methods.