强连通有向图上共识的广播八卦算法
Broadcast Gossip Algorithms for Consensus on Strongly Connected Digraphs
AI总结：
本文提出一种使用伴随变量的广播八卦算法框架，通过异步迭代在强连通有向图上实现平均共识，并利用非负矩阵理论和摄动理论分析收敛性。
摘要：
我们研究了一个使用伴随变量解决平均共识问题的广播八卦算法的一般框架。每个节点维护一个初始状态和一个伴随变量。迭代更新是异步进行的，其中一个随机节点广播其当前状态和伴随变量，所有其他接收广播的节点更新其状态和伴随变量。我们提供了该方案在任意强连通有向图上保证收敛到共识解的条件，其中所有节点具有相同的极限值。在更强的条件下（当底层通信图是无向图时合理），我们保证共识值等于平均值，无论是在期望意义下还是在均方意义下。我们的分析使用了非负矩阵理论和摄动理论的工具。摄动结果依赖于一个参数足够小。我们刻画了允许的上界以及摄动参数相对于网络拓扑的最优设置，这使我们能够刻画最坏情况下的收敛速率。仿真表明，与现有的广播八卦算法相比，本文提出的方法具有同时保证收敛到平均共识和以较少广播次数收敛的优势。
英文摘要：
We study a general framework for broadcast gossip algorithms which use companion variables to solve the average consensus problem. Each node maintains an initial state and a companion variable. Iterative updates are performed asynchronously whereby one random node broadcasts its current state and companion variable and all other nodes receiving the broadcast update their state and companion variable. We provide conditions under which this scheme is guaranteed to converge to a consensus solution, where all nodes have the same limiting values, on any strongly connected directed graph. Under stronger conditions, which are reasonable when the underlying communication graph is undirected, we guarantee that the consensus value is equal to the average, both in expectation and in the mean-squared sense. Our analysis uses tools from non-negative matrix theory and perturbation theory. The perturbation results rely on a parameter being sufficiently small. We characterize the allowable upper bound as well as the optimal setting for the perturbation parameter as a function of the network topology, and this allows us to characterize the worst-case rate of convergence. Simulations illustrate that, in comparison to existing broadcast gossip algorithms, the approaches proposed in this paper have the advantage that they simultaneously can be guaranteed to converge to the average consensus and they converge in a small number of broadcasts.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
