Optimal transport divergences induced by scoring functions

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2024-07-24 DOI:10.1016/j.orl.2024.107146

Silvana M. Pesenti , Steven Vanduffel

引用次数: 0

Abstract

We employ scoring functions, used in statistics for eliciting risk functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport problem. This gives rise to a rich variety of novel asymmetric MK divergences, subsuming Bregman-Wasserstein divergences. We show that for distributions on the real line, the comonotonic coupling is optimal for the majority of the new divergences. We conclude with two applications to robust optimisation.

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由评分函数引起的最佳传输分歧

我们在蒙日-康托洛维奇（MK）最优传输问题中采用了统计学中用于激发风险函数的评分函数作为成本函数。这就产生了丰富多样的新型非对称 MK 发散，包含了 Bregman-Wasserstein 发散。我们的研究表明，对于实线上的分布，对于大多数新发散而言，协约耦合是最优的。最后，我们将介绍稳健优化的两个应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

期刊介绍： Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.