A distributional interpretation of robust optimization

Motivated by data-driven decision making and sampling problems, we investigate probabilistic interpretations of Robust Optimization (RO). We establish a connection between RO and Distributionally Robust Stochastic Programming (DRSP), showing that the solution to any RO problem is also a solution to a DRSP problem. Specifically, we consider the case where multiple uncertain parameters belong to the same fixed dimensional space, and find the set of distributions of the equivalent DRSP. The equivalence we derive enables us to construct RO formulations that are statistically consistent, and in the process, provides a systematic approach for tuning the uncertainty set.