2019/10/18 by Mikael Johansson, Mai, Vien V., Johansson, Mikael · 7 citations
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Matrix Theory and Algorithms #Numerical methods in inverse problems #Optimization and Control (math.OC) #Radiative Heat Transfer Studies
paper · pdf · doi:10.48550/arxiv.1910.08590
openalex publication_date 2019/10/18 · openalex created_date 2020/06/19 · openalex updated_date 2026/07/28
Anderson acceleration is a well-established and simple technique for speeding up fixed-point computations with countless applications. Previous studies of Anderson acceleration in optimization have only been able to provide convergence guarantees for unconstrained and smooth problems. This work introduces novel methods for adapting Anderson acceleration to (non-smooth and constrained) proximal gradient algorithms. Under some technical conditions, we extend the existing local convergence results of Anderson acceleration for smooth fixed-point mappings to the proposed scheme. We also prove analytically that it is not, in general, possible to guarantee global convergence of native Anderson acceleration. We therefore propose a simple scheme for stabilization that combines the global worst-case guarantees of proximal gradient methods with the local adaptation and practical speed-up of Anderson acceleration.