文章基本信息

标题：Convergence Analysis on Data-Driven Fortet-Mourier Metrics with Applications in Stochastic Optimization
本地全文：下载
作者：Zhiping Chen ; He Hu ; Jie Jiang 等
期刊名称：Sustainability
印刷版ISSN：2071-1050
出版年度：2022
卷号：14
期号：8
页码：4501
DOI：10.3390/su14084501
语种：English
出版社：MDPI, Open Access Journal
摘要：Fortet-Mourier (FM) probability metrics are important probability metrics, which have been widely adopted in the quantitative stability analysis of stochastic programming problems. In this study, we contribute to different types of convergence assertions between a probability distribution and its empirical distribution when the deviation is measured by FM metrics and consider their applications in stochastic optimization. We first establish the quantitative relation between FM metrics and Wasserstein metrics. After that, we derive the non-asymptotic moment estimate, asymptotic convergence, and non-asymptotic concentration estimate for FM metrics, which supplement the existing results. Finally, we apply the derived results to four kinds of stochastic optimization problems, which either extend the present results to more general cases or provide alternative avenues. All these discussions demonstrate the motivation as well as the significance of our study.