参数估计的分布式BFGS算法设计及大样本性质

Design of Distributed BFGS Algorithm and Large Sample Properties for Parameter Estimation

在分布式条件下,为了缩减通信成本,本文基于BPGS拟牛顿法解决了相应的分布式算法设计与统计推断问题.在较低的通信成本下,本文建立了快速分布式BFGS算法,其关键是将步长进行分布式近似计算;从理论上证明了当迭代次数满足一定条件时,所得的BFGS估计量具有一致性和渐近正态性,并且给出了一个方差估计公式.通过模拟实验验证了本文基本理论的正确性,同时验证了分布式BFGS方法的估计效果与集中式方法十分接近,从而进一步说明该方法的有效性.

Under the distributed condition,in order to reduce the cost of communication,this paper solves problems of the corresponding distributed algorithm design and statistical inference based on the BFGS quasi-Newton method.With lower communication cost,a fast distributed BFGS algorithm is established.The key of this algorithm is to perform a distributed approximate calculation of the step size.It is theoretically proved that when the number of iterations meets some conditions,the BFGS estimator is consistent and asymptotically normal.And we propose a estimation formula of variance.The experiment verifies the correctness of the basic theory in this article.At the same time it is showed that the estimation accuracy of the distributed BFGS method is very close to that of the centralized method,which further illustrates the effectiveness of the method.