2022/01/11 by Yichuan Li, Li, Yichuan, Petros G. Voulgaris +3
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Distributed Control Multi-Agent Systems #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2201.03759
openalex publication_date 2022/01/11 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We propose a communication efficient quasi-Newton method for large-scale multi-agent convex composite optimization. We assume the setting of a network of agents that cooperatively solve a global minimization problem with strongly convex local cost functions augmented with a non-smooth convex regularizer. By introducing consensus variables, we obtain a block-diagonal Hessian and thus eliminate the need for additional communication when approximating the objective curvature information. Moreover, we reduce computational costs of existing primal-dual quasi-Newton methods from O(d3) to O(cd) by storing c pairs of vectors of dimension d. An asynchronous implementation is presented that removes the need for coordination. Global linear convergence rate in expectation is established, and we demonstrate the merit of our algorithm numerically with real datasets.