# Learning-based Robust Optimization: Procedures and Statistical Guarantees

## TL;DR

This paper introduces a statistical framework for robust optimization that uses data-driven prediction sets with finite-sample guarantees, ensuring feasibility independent of problem dimensions.

## Contribution

It develops a novel data-driven robust optimization method with dimension-free statistical guarantees and simple validation procedures.

## Key findings

- Sample size for feasibility is independent of decision and probability space dimensions.
- The method provides finite-sample, nonparametric guarantees on feasibility.
- Approaches to improve objective performance while maintaining guarantees are discussed.

## Abstract

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.