有向网络中一种快速的分布式随机算法  

A Fast Distributed Stochastic Algorithm over Directed Networks

作　　者：宫秀慧 

机构地区：[1]河北工业大学理学院,天津

出　　处：《应用数学进展》2024年第2期848-868,共21页Advances in Applied Mathematics

摘　　要：本文考虑有向网络上多智能体系统中的分布式优化问题。 其全局目标函数可表示为网络中所有局 部目标函数有限和的形式。 通过利用 Nesterov 动量技巧方法和单循环的方差缩减技术 LSVRG, 本文提出了有向网络中一种快速的分布式随机算法 AB-LSVRG。 对光滑和强凸的目标函数,理 论分析证明所提出的算法可以线性收敛到最优解。 基于分布式逻辑回归问题,数值实验表明本文 所提出的算法与现有的一些分布式算法相比表现效果更好。This paper considers the distributed optimization in a multi-agent system over bal- anced directed networks. The global objective function describes a finite sum of all local objective functions on the networks. Combining the distributed loopless variancereduction method with Nesterov momentum strategy, a fast distributed stochastic al- gorithm is developed, named ABN-LSVRG. For smooth and strongly convex objective functions, it is proved that ABN-LSVRG has a linear convergence rate. Based on the distributed logistic problem, simulation results show that ABN-LSVRG performs bet- ter in comparison with some distributed algorithms.

关 键 词：分布式优化 多智能系统 有向网络 分布式方差缩减 动量加速 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]