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This paper studies two-stage distributionally robust conic linear programmingunder constraint uncertainty over type-1 Wasserstein balls. We presentoptimality conditions for the dual of the worst-case expectation problem, whichcharacterizes worst-case uncertain parameters for its inner maximizationproblem. The proposed optimality conditions suggest binary representations ofuncertain parameters supported on a hyperrectangle, which allows a Benders-likecut generation procedure that attains $\epsilon$-optimality in a finite numberof iterations. These conditions also lead to an interesting analysis of aspecial case in which the support of the uncertain parameters is unconstrained:the inner maximization problem in the dual of the worst-case expectationproblem reduces to sample average approximation (SAA), which extends previouswork reported in the literature. For the case of convex conic supports, wepresent a counterexample that shows the SAA solution may become suboptimal tothe inner maximization problem, contrary to previous claims.

Two-Stage Distributionally Robust Conic Linear Programming over 1-Wasserstein Balls