论文标题
关于随机共识算法中噪声的影响
On the Influence of Noise in Randomized Consensus Algorithms
论文作者
论文摘要
在本文中，我们研究了随机共识算法中加性噪声的影响。假设更新矩阵是对称的，我们会为噪声引起的均方根误差提供封闭形式的表达式，以及更简单的评估上限和下限。通过研究开放多代理系统的研究，我们集中于随机引起的离散的拉普拉斯族，这是一个由大型无向图的采样子图产生的更新矩阵家族。对于这些矩阵，我们通过使用基础图的拉普拉斯矩阵的特征值或图形的平均有效电阻，从而证明其紧密度。最后，我们在某些图的示例中得出了界限的表达式，并对它们进行了数字评估。
In this paper we study the influence of additive noise in randomized consensus algorithms. Assuming that the update matrices are symmetric, we derive a closed form expression for the mean square error induced by the noise, together with upper and lower bounds that are simpler to evaluate. Motivated by the study of Open Multi-Agent Systems, we concentrate on Randomly Induced Discretized Laplacians, a family of update matrices that are generated by sampling subgraphs of a large undirected graph. For these matrices, we express the bounds by using the eigenvalues of the Laplacian matrix of the underlying graph or the graph's average effective resistance, thereby proving their tightness. Finally, we derive expressions for the bounds on some examples of graphs and numerically evaluate them.
