  Robust optimization (RO) is a common approach to tractably obtain
safeguarding solutions for optimization problems with uncertain constraints. In
this paper, we study a statistical framework to integrate data into RO, based
on learning a prediction set using (combinations of) geometric shapes that are
compatible with established RO tools, and a simple data-splitting validation
step that achieves finite-sample nonparametric statistical guarantees on
feasibility. We demonstrate how our required sample size to achieve feasibility
at a given confidence level is independent of the dimensions of both the
decision space and the probability space governing the stochasticity, and
discuss some approaches to improve the objective performances while maintaining
these dimension-free statistical feasibility guarantees.
