TY - JOUR
T1 - On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls
AU - Chen, Zhi
AU - Kuhn, Daniel
AU - Wiesemann, Wolfram
PY - 2023/5
Y1 - 2023/5
N2 - 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.© 2023 Elsevier B.V. All rights reserved.
AB - 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.© 2023 Elsevier B.V. All rights reserved.
KW - Distributionally robust optimization
KW - Ambiguous chance constraints
KW - Wasserstein distance
KW - Conditional value-at-risk
KW - Bonferroni’s inequality
KW - ALSO-X approximation
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85150351230&origin=recordpage
U2 - 10.1016/j.orl.2023.02.008
DO - 10.1016/j.orl.2023.02.008
M3 - 21_Publication in refereed journal
VL - 51
SP - 226
EP - 233
JO - Operations Research Letters
JF - Operations Research Letters
SN - 0167-6377
IS - 3
ER -