Accelerated Gradient

Accelerated gradient methods aim to speed up the convergence of gradient descent algorithms used in optimization problems, particularly in machine learning. Current research focuses on extending these methods to non-convex settings, such as those encountered in training deep neural networks, and improving their theoretical understanding, including convergence rates and stability analysis, often employing variations of Nesterov's Accelerated Gradient and Polyak's Heavy Ball methods. These advancements are significant because faster optimization algorithms translate to reduced computational costs and improved efficiency in various applications, from reinforcement learning to solving large-scale optimization problems in engineering and science.