Solving Wasserstein Robust Two-stage Stochastic Linear Programs via Second-order Conic Programming

This paper proposes a novel data-driven distributionally robust (DR) two-stage linear program over the 1-Wasserstein ball to handle the stochastic uncertainty with unknown distribution. We study the case with distribution uncertainty only in the objective function. In sharp contrast to the exiting literature, our model can be equivalently reformulated as a solvable second-order cone programming (SOCP) problem. Moreover, the distribution achieving the worst-case cost is given as an "empirical"distribution by simply perturbing each sample and the asymptotic convergence of the proposed model is also proved. Finally, experiments illustrate the advantages of our model in terms of the out-of-sample performance and computational complexity.