On the Optimality of Affine Decision Rules in Distributionally Robust Optimization

We propose conditions under which two-stage distributionally robust optimization problems are optimally solved in affine or K -adaptable affine decision rules. Contrary to previous work, our conditions do not impose any structure on the support of the uncertain parameters, and they ensure pointwise (as opposed to worst case) optimality of ( K -adaptable) affine decision rules. The absence of support restrictions allows us to transfer nonlinearities from the problem description to the support via liftings, whereas the pointwise optimality implies that decision rules remain optimal for broad classes of distributionally robust optimization problems, including data-driven problems over ϕ -divergence or Wasserstein ambiguity sets. We demonstrate how our conditions can be met in two applications.