On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)226-233
Journal / PublicationOperations Research Letters
Volume51
Issue number3
Online published25 Feb 2023
Publication statusPublished - May 2023

Abstract

Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affecting the safety condition(s) is only known to belong to some ambiguity set. We study three popular approximation schemes for distributionally robust chance constrained programs over Wasserstein balls, where the ambiguity set contains all probability distributions within a certain Wasserstein distance to a reference distribution. The first approximation replaces the chance constraint with a bound on the conditional value-at-risk, the second approximation decouples different safety conditions via Bonferroni's inequality, and the third approximation restricts the expected violation of the safety condition(s) so that the chance constraint is satisfied. We show that the conditional value-at-risk approximation can be characterized as a tight convex approximation, which complements earlier findings on classical (non-robust) chance constraints, and we offer a novel interpretation in terms of transportation savings. We also show that the three approximations can perform arbitrarily poorly in data-driven settings, and that they are generally incomparable with each other.

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Research Area(s)

  • Distributionally robust optimization, Ambiguous chance constraints, Wasserstein distance, Conditional value-at-risk, Bonferroni’s inequality, ALSO-X approximation

Citation Format(s)

On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls. / Chen, Zhi; Kuhn, Daniel; Wiesemann, Wolfram.
In: Operations Research Letters, Vol. 51, No. 3, 05.2023, p. 226-233.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review