2019/06/18 by Saverio Salzo, Silvia Villa, Salzo, Saverio +1 · 1 citation
Computer Science · Mathematics · #49M27 #65K05 #90C06 #90C25 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1906.07392
openalex publication_date 2019/06/18 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We study the block-coordinate forward-backward algorithm in which the blocks\nare updated in a random and possibly parallel manner, according to arbitrary\nprobabilities. The algorithm allows different stepsizes along the\nblock-coordinates to fully exploit the smoothness properties of the objective\nfunction. In the convex case and in an infinite dimensional setting, we\nestablish almost sure weak convergence of the iterates and the asymptotic rate\no(1/n) for the mean of the function values. We derive linear rates under strong\nconvexity and error bound conditions. Our analysis is based on an abstract\nconvergence principle for stochastic descent algorithms which allows to extend\nand simplify existing results.\n