An introduction to distributionally robust optimization

Initially developed in 1937, Operational Research focused on constructing deterministic models in order to describe and analyze real-world problems to aid decision-making. It was not until the early 1950s when uncertainty was incorporated into these models. Traditionally, two primary disciplines have been employed: Stochastic Optimization (SO) and Robust Optimization (RO). In SO, uncertain parameters are modeled as random variables with known probability distributions. However, there has been significant criticism of its optimistic results in recent years. In contrast, RO addresses uncertainty by considering the worst-case scenarios, leading to over-conservative decisions for other more likely scenarios. An emerging paradigm Distributionally Robust Optimization (DRO) has recently garnered significant attention due to its potential to address the limitations of both SO and RO. DRO serves as a unifying framework by introducing the concept of an ambiguity set, which encompasses a family of distributions deemed close-enough to a reference distribution.