Steepest Descent

Steepest descent is a fundamental optimization method aiming to find the minimum of a function by iteratively moving in the direction of the negative gradient. Current research focuses on extending its applicability beyond Euclidean spaces, exploring accelerated variants with improved convergence rates under various smoothness assumptions, and analyzing its implicit bias in machine learning contexts, particularly concerning the impact of different norms and regularization techniques like weight decay. These advancements are significant because they enhance the efficiency and effectiveness of steepest descent in diverse applications, including training deep neural networks and solving inverse problems, leading to improved performance and a deeper theoretical understanding of optimization algorithms.