Iteration Complexity

Iteration complexity, a crucial metric in optimization algorithms, focuses on determining the number of iterations needed to achieve a solution within a specified error tolerance. Current research emphasizes improving iteration complexity for various optimization problems, including convex, nonconvex, minimax, and bilevel problems, often employing techniques like accelerated gradient descent, momentum methods, and proximal algorithms, sometimes adapted for decentralized or federated learning settings. These advancements are significant because reduced iteration complexity translates to faster training times and improved efficiency in machine learning, particularly for large-scale datasets and complex models. This directly impacts the feasibility and scalability of numerous applications across diverse fields.