Distributions with Maximum Spread Subject to Wasserstein Distance Constraints

• Published in: Journal of the Operations Research Society of China (Internet) Vol. 7; no. 1; pp. 69 - 105
• Main Authors: Carlsson, John Gunnar, Wang, Ye
• Format: Journal Article
• Language: English
• Published: Beijing Operations Research Society of China 01.03.2019; Springer Nature B.V
• Subjects: Aircraft; Ambiguity; Covariance matrix; Drones; Entropy; Management Science; Mathematics; Mathematics and Statistics; Operations Research; Probability; Probability distribution; Random variables; Surveillance; Unmanned aerial vehicles; 90C15; Surveillance; Districting; Distributionally robust optimization; 90C34
• ISSN: 2194-668X; 2194-6698
• DOI: 10.1007/s40305-018-00238-5

Recent research on formulating and solving distributionally robust optimization problems has seen many different approaches for describing one’s ambiguity set, such as constraints on first and second moments or quantiles. In this paper, we use the Wasserstein distance to characterize the ambiguity set of distributions, which allows us to circumvent common overestimation that arises when other procedures are used, such as fixing the center of mass and the covariance matrix of the distribution. In particular, we derive closed-form expressions for distributions that are as “spread out” as possible, and apply our result to a problem in multi-vehicle coordination.