论文标题
使用缓冲信息最快的线性收敛离散时间平均共识
The fastest linearly converging discrete-time average consensus using buffered information
论文作者
论文摘要
在这封信中，我们研究了在离散时间通信设置中加速与连接图的平均共识的问题。文献表明，可以通过增加图形连接性或优化代理在从其邻居接收的信息上进行优化的权重来加速共识算法。在这封信中而不是更改通信图中，我们研究了两种使用缓冲状态加速给定图的平均共识的方法。在第一种方法中，我们研究了众所周知的一阶拉普拉斯平均共识算法的收敛速率如何随延迟反馈而变化，并在延迟范围内获得足够的条件，从而导致更快的收敛性。在第二个提出的方法中，我们展示了如何将平均共识问题作为凸优化问题施加，并通过一阶加速优化算法来解决强大的成本函数。我们使用所谓的三重动量优化算法构建最快的收敛平均共识算法。我们使用网络内线性回归问题证明了结果，该问题被认为是两个平均共识问题。
In this letter, we study the problem of accelerating reaching average consensus over connected graphs in a discrete-time communication setting. Literature has shown that consensus algorithms can be accelerated by increasing the graph connectivity or optimizing the weights agents place on the information received from their neighbors. In this letter instead of altering the communication graph, we investigate two methods that use buffered states to accelerate reaching average consensus over a given graph. In the first method, we study how convergence rate of the well-known first-order Laplacian average consensus algorithm changes with delayed feedback and obtain a sufficient condition on the ranges of delay that leads to faster convergence. In the second proposed method, we show how average consensus problem can be cast as a convex optimization problem and solved by first-order accelerated optimization algorithms for strongly-convex cost functions. We construct the fastest converging average consensus algorithm using the so-called Triple Momentum optimization algorithm. We demonstrate our results using an in-network linear regression problem, which is formulated as two average consensus problems.
