Halpern Iteration

Halpern iteration is an iterative method for finding fixed points of nonexpansive operators, a problem arising in diverse fields like image processing, reinforcement learning, and optimization. Current research focuses on improving its efficiency and convergence rates, particularly through variance reduction techniques and inexact variants, leading to algorithms with better complexity bounds for solving monotone inclusion problems and related tasks. These advancements are impacting various applications by enabling faster and more robust solutions to challenging optimization problems in machine learning and beyond.