Solving Wasserstein Robust Two-stage Stochastic Linear Programs via Second-order Conic Programming

Zhuolin Wang; Keyou You; Shiji Song; Yuli Zhang

doi:10.23919/CCC52363.2021.9549657

Solving Wasserstein Robust Two-stage Stochastic Linear Programs via Second-order Conic Programming

Zhuolin Wang, Keyou You^*, Shiji Song, Yuli Zhang

^*Corresponding author for this work

Tsinghua University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper proposes a novel data-driven distributionally robust (DR) two-stage linear program over the 1-Wasserstein ball to handle the stochastic uncertainty with unknown distribution. We study the case with distribution uncertainty only in the objective function. In sharp contrast to the exiting literature, our model can be equivalently reformulated as a solvable second-order cone programming (SOCP) problem. Moreover, the distribution achieving the worst-case cost is given as an "empirical"distribution by simply perturbing each sample and the asymptotic convergence of the proposed model is also proved. Finally, experiments illustrate the advantages of our model in terms of the out-of-sample performance and computational complexity.

Original language	English
Title of host publication	Proceedings of the 40th Chinese Control Conference, CCC 2021
Editors	Chen Peng, Jian Sun
Publisher	IEEE Computer Society
Pages	1875-1880
Number of pages	6
ISBN (Electronic)	9789881563804
DOIs	https://doi.org/10.23919/CCC52363.2021.9549657
Publication status	Published - 26 Jul 2021
Event	40th Chinese Control Conference, CCC 2021 - Shanghai, China Duration: 26 Jul 2021 → 28 Jul 2021

Publication series

Name	Chinese Control Conference, CCC
Volume	2021-July
ISSN (Print)	1934-1768
ISSN (Electronic)	2161-2927

Conference

Conference	40th Chinese Control Conference, CCC 2021
Country/Territory	China
City	Shanghai
Period	26/07/21 → 28/07/21

Keywords

Wasserstein ball
data-driven robust
distribution uncertainty
two-stage linear program

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10.23919/CCC52363.2021.9549657

Cite this

Wang, Z., You, K., Song, S., & Zhang, Y. (2021). Solving Wasserstein Robust Two-stage Stochastic Linear Programs via Second-order Conic Programming. In C. Peng, & J. Sun (Eds.), Proceedings of the 40th Chinese Control Conference, CCC 2021 (pp. 1875-1880). (Chinese Control Conference, CCC; Vol. 2021-July). IEEE Computer Society. https://doi.org/10.23919/CCC52363.2021.9549657

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title = "Solving Wasserstein Robust Two-stage Stochastic Linear Programs via Second-order Conic Programming",

abstract = "This paper proposes a novel data-driven distributionally robust (DR) two-stage linear program over the 1-Wasserstein ball to handle the stochastic uncertainty with unknown distribution. We study the case with distribution uncertainty only in the objective function. In sharp contrast to the exiting literature, our model can be equivalently reformulated as a solvable second-order cone programming (SOCP) problem. Moreover, the distribution achieving the worst-case cost is given as an {"}empirical{"}distribution by simply perturbing each sample and the asymptotic convergence of the proposed model is also proved. Finally, experiments illustrate the advantages of our model in terms of the out-of-sample performance and computational complexity.",

keywords = "Wasserstein ball, data-driven robust, distribution uncertainty, two-stage linear program",

author = "Zhuolin Wang and Keyou You and Shiji Song and Yuli Zhang",

note = "Publisher Copyright: {\textcopyright} 2021 Technical Committee on Control Theory, Chinese Association of Automation.; 40th Chinese Control Conference, CCC 2021 ; Conference date: 26-07-2021 Through 28-07-2021",

year = "2021",

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day = "26",

doi = "10.23919/CCC52363.2021.9549657",

language = "English",

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editor = "Chen Peng and Jian Sun",

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}

Wang, Z, You, K, Song, S & Zhang, Y 2021, Solving Wasserstein Robust Two-stage Stochastic Linear Programs via Second-order Conic Programming. in C Peng & J Sun (eds), Proceedings of the 40th Chinese Control Conference, CCC 2021. Chinese Control Conference, CCC, vol. 2021-July, IEEE Computer Society, pp. 1875-1880, 40th Chinese Control Conference, CCC 2021, Shanghai, China, 26/07/21. https://doi.org/10.23919/CCC52363.2021.9549657

Solving Wasserstein Robust Two-stage Stochastic Linear Programs via Second-order Conic Programming. / Wang, Zhuolin; You, Keyou; Song, Shiji et al.
Proceedings of the 40th Chinese Control Conference, CCC 2021. ed. / Chen Peng; Jian Sun. IEEE Computer Society, 2021. p. 1875-1880 (Chinese Control Conference, CCC; Vol. 2021-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Solving Wasserstein Robust Two-stage Stochastic Linear Programs via Second-order Conic Programming

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AU - You, Keyou

AU - Song, Shiji

AU - Zhang, Yuli

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N2 - This paper proposes a novel data-driven distributionally robust (DR) two-stage linear program over the 1-Wasserstein ball to handle the stochastic uncertainty with unknown distribution. We study the case with distribution uncertainty only in the objective function. In sharp contrast to the exiting literature, our model can be equivalently reformulated as a solvable second-order cone programming (SOCP) problem. Moreover, the distribution achieving the worst-case cost is given as an "empirical"distribution by simply perturbing each sample and the asymptotic convergence of the proposed model is also proved. Finally, experiments illustrate the advantages of our model in terms of the out-of-sample performance and computational complexity.

AB - This paper proposes a novel data-driven distributionally robust (DR) two-stage linear program over the 1-Wasserstein ball to handle the stochastic uncertainty with unknown distribution. We study the case with distribution uncertainty only in the objective function. In sharp contrast to the exiting literature, our model can be equivalently reformulated as a solvable second-order cone programming (SOCP) problem. Moreover, the distribution achieving the worst-case cost is given as an "empirical"distribution by simply perturbing each sample and the asymptotic convergence of the proposed model is also proved. Finally, experiments illustrate the advantages of our model in terms of the out-of-sample performance and computational complexity.

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KW - distribution uncertainty

KW - two-stage linear program

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Solving Wasserstein Robust Two-stage Stochastic Linear Programs via Second-order Conic Programming

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