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.

研究了三种分布鲁棒的机会限制规划的近似方案，并且在数据驱动的环境下表现得差别很大。其中一种方案采用条件风险价值的紧凑凸估计，并提供了一种新颖的解释方式。同时，他们的优劣无法相互比较。