Distributed mirror descent method for multi-agent optimization with delay
Distributed mirror descent method for multi-agent optimization with delay
复制标题
延迟多智能体优化的分布式镜像下降法
DOI：
10.1016/j.neucom.2015.12.017
复制
发表时间：
2016
期刊：
影响因子：
6
通讯作者：
Wu Zhiyou
中科院分区：
文献类型：
--
作者：
Li Jueyou;Chen Guo;Dong Zhaoyang;Wu Zhiyou
本文研究了与存在延迟的时变多智能体网络相关的分布式优化问题，其中每个智能体都可以本地访问其凸目标函数，并协作最小化网络上智能体的凸目标函数之和。基于镜像下降法，我们开发了一种分布式算法，通过探索延迟梯度信息来解决这个问题。此外，我们分析了延迟梯度对算法收敛的影响，并提供了作为延迟参数、网络大小和拓扑函数的收敛速度的明确界限。我们的结果表明，对于平滑问题，延迟是渐近可以忽略不计的。所提出的算法可以被视为分布式基于梯度的投影方法的推广，因为它利用定制的布雷格曼散度而不是通常的欧几里得平方距离。最后，给出了逻辑回归问题的一些仿真结果来证明该算法的有效性。
This paper investigates a distributed optimization problem associated a time-varying multi-agent network with the presence of delays, where each agent has local access to its convex objective function, and cooperatively minimizes a sum of convex objective functions of the agents over the network. Based on the mirror descent method, we develop a distributed algorithm to solve this problem by exploring the delayed gradient information. Furthermore, we analyze the effects of delayed gradients on the convergence of the algorithm and provide an explicit bound on the convergence rate as a function of the delay parameter, the network size and topology. Our results show that the delays are asymptotically negligible for smooth problems. The proposed algorithm can be viewed as a generalization of the distributed gradient-based projection methods since it utilizes a customized Bregman divergence instead of the usual Euclidean squared distance. Finally, some simulation results on a logistic regression problem are presented to demonstrate the effectiveness of the algorithm.