Distributions with Maximum Spread Subject to Wasserstein Distance Constraints
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 s...
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| Published in | Journal of the Operations Research Society of China (Internet) Vol. 7; no. 1; pp. 69 - 105 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Beijing
Operations Research Society of China
01.03.2019
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2194-668X 2194-6698 |
| DOI | 10.1007/s40305-018-00238-5 |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Wang, Ye Carlsson, John Gunnar |
| Author_xml | – sequence: 1 givenname: John Gunnar surname: Carlsson fullname: Carlsson, John Gunnar email: jcarlsso@usc.edu organization: University of Southern California – sequence: 2 givenname: Ye surname: Wang fullname: Wang, Ye organization: University of Southern California |
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| Cites_doi | 10.5802/afst.1095 10.1007/s10957-006-9084-x 10.1007/s10107-005-0678-0 10.1111/j.1937-5956.2012.01420.x 10.1103/PhysRev.106.620 10.1287/opre.2013.1160 10.1007/s00440-014-0583-7 10.1287/opre.2014.1323 10.1287/opre.1090.0795 10.1137/060654803 10.1287/opre.1100.0821 10.1023/A:1026543900054 10.1109/MRA.2009.932528 10.1287/opre.2018.1746 10.1287/opre.1090.0741 10.1007/s10107-011-0494-7 10.1090/gsm/058 10.1080/1055678021000060829a 10.1287/mnsc.1120.1641 10.1287/opre.1060.0353 10.1080/14697680701455410 10.1007/978-0-8176-4679-0 10.1287/moor.1040.0129 10.1007/s10479-010-0812-0 10.1016/j.trb.2015.02.001 10.1287/opre.1070.0441 10.1007/3-540-34416-0_20 10.1007/978-3-642-40020-9_62 10.1007/s41884-018-0002-8 10.1007/s00440-006-0004-7 10.1080/00031305.1996.10474359 |
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| SubjectTerms | Aircraft Ambiguity Covariance matrix Drones Entropy Management Science Mathematics Mathematics and Statistics Operations Research Probability Probability distribution Random variables Surveillance Unmanned aerial vehicles |
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| Title | Distributions with Maximum Spread Subject to Wasserstein Distance Constraints |
| URI | https://link.springer.com/article/10.1007/s40305-018-00238-5 https://www.proquest.com/docview/2932313839 |
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