Parallel random block-coordinate forward-backward algorithm: a unified convergence analysis

• 成果类型: Article
• 署名作者: Salzo, Saverio; Villa, Silvia
• 署名单位: Istituto Italiano di Tecnologia - IIT; University of Genoa
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01602-1
• 发表日期: 2022
• 页码: 225-269
• 关键词: descent methods; optimization

摘要

We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to fully exploit the smoothness properties of the objective function. In the convex case and in an infinite dimensional setting, we establish almost sure weak convergence of the iterates and the asymptotic rate o(1/n) for the mean of the function values. We derive linear rates under strong convexity and error bound conditions. Our analysis is based on an abstract convergence principle for stochastic descent algorithms which allows to extend and simplify existing results.