Decentralized Asynchronous Nonconvex Stochastic Optimization on Directed Graphs

作     者：Kungurtsev, Vyacheslav Morafah, Mahdi Javidi, Tara Scutari, Gesualdo 

作者机构：Czech Tech Univ Dept Comp Sci Prague Czech Republic Univ Calif San Diego Dept Elect Engn La Jolla CA 92093 USA Purdue Univ Sch Ind Engn W Lafayette IN 47907 USA 

出 版 物：《IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS》 (IEEE Trans. Control Netw. Syst.)

年 卷 期：2023年第10卷第4期

页      面：1796-1804页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：OP VVV 

主　　题：Optimization Stochastic processes Convergence Delays Directed graphs Noise measurement Linear programming Decentralized applications distributed computing federated learning machine learning optimization optimization methods 

摘      要：In this article, we consider a decentralized stochastic optimization problem over a network of agents, modeled as a directed graph: Agents aim to asynchronously minimize the average of their individual losses (possibly nonconvex), each one having access only to a noisy estimate of the gradient of its own function. We propose an asynchronous distributed algorithm for such a class of problems. The algorithm combines stochastic gradients with tracking in an asynchronous push-sum framework and obtains a sublinear convergence rate, matching the rate of the centralized stochastic gradient descent applied to the nonconvex minimization. Our experiments on a nonconvex image classification task using a convolutional neural network validate the convergence of our proposed algorithm across a different number of nodes and graph connectivity percentages.