On approximations of data-driven chance constrained programs over Wasserstein balls

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