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On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls | | Zhi Chen
; Daniel Kuhn
; Wolfram Wiesemann
; | | Date: |
1 Jun 2022 | | 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 two 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,
whereas the second approximation decouples different safety conditions via
Bonferroni’s inequality. 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 two approximation schemes can both perform arbitrarily poorly in
data-driven settings, and that they are generally incomparable with each other
-- in contrast to earlier results for moment-based ambiguity sets. | | Source: | arXiv, 2206.00231 | | Services: | Forum | Review | PDF | Favorites | |
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