2020/07/07 by César A. Uribe, Uribe, César A., Ali Jadbabaie +1
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Multiagent Systems (cs.MA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2007.03562
openalex publication_date 2020/07/07 · openalex created_date 2020/07/10 · openalex updated_date 2026/07/28
We propose a distributed, cubic-regularized Newton method for large-scale convex optimization over networks. The proposed method requires only local computations and communications and is suitable for federated learning applications over arbitrary network topologies. We show a O(k^-3) convergence rate when the cost function is convex with Lipschitz gradient and Hessian, with k being the number of iterations. We further provide network-dependent bounds for the communication required in each step of the algorithm. We provide numerical experiments that validate our theoretical results.