Super Gradient Descent: Global Optimization requires Global Gradient
This work provides a solution for global optimization in machine learning, particularly for line search, but is incremental as it focuses on one-dimensional functions.
The paper tackles the problem of global minimization in optimization by introducing Super Gradient Descent, a method that guarantees convergence to the global minimum for any k-Lipschitz one-dimensional function on a closed interval, addressing limitations of traditional algorithms that get trapped in local minima.
Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization method that we called Super Gradient Descent, designed specifically for one-dimensional functions, guaranteeing convergence to the global minimum for any k-Lipschitz function defined on a closed interval [a, b]. Our approach addresses the limitations of traditional optimization algorithms, which often get trapped in local minima. In particular, we introduce the concept of global gradient which offers a robust solution for precise and well-guided global optimization. By focusing on the global minimization problem, this work bridges a critical gap in optimization theory, offering new insights and practical advancements in different optimization problems in particular Machine Learning problems like line search.