2021/10/28 by Brighton Ancelin, Ancelin, Brighton, Sohail Bahmani +3
Computer Science · Engineering · #Distributed Control Multi-Agent Systems #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Mathematics #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.2110.15283
openalex publication_date 2021/10/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We consider the "all-for-one" decentralized learning problem for generalized\nlinear models. The features of each sample are partitioned among several\ncollaborating agents in a connected network, but only one agent observes the\nresponse variables. To solve the regularized empirical risk minimization in\nthis distributed setting, we apply the Chambolle--Pock primal--dual algorithm\nto an equivalent saddle-point formulation of the problem. The primal and dual\niterations are either in closed-form or reduce to coordinate-wise minimization\nof scalar convex functions. We establish convergence rates for the empirical\nrisk minimization under two different assumptions on the loss function\n(Lipschitz and square root Lipschitz), and show how they depend on the\ncharacteristics of the design matrix and the Laplacian of the network.\n