# Learning-based Robust Optimization: Procedures and Statistical Guarantees

arXiv: https://arxiv.org/abs/1704.04342 · HTML: https://mlsanity.com/paper/1704.04342/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2017.

## Built on by (most cited first, 9 of 9)

- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [Analytics and Machine Learning in Vehicle Routing Research](https://mlsanity.com/paper/2102.10012/) (2021)
- [On the Foundation of Distributionally Robust Reinforcement Learning](https://mlsanity.com/paper/2311.09018/) (2023)
- [Regret Equals Covariance: A Closed-Form Characterization for Stochastic Optimization](https://mlsanity.com/paper/2605.14019/) (2026)
- [Neural Network Layers for Prediction of Positive Definite Elastic Stiffness Tensors](https://mlsanity.com/paper/2203.13938/) (2022)
- [A Deep Generative Learning Approach for Two-stage Adaptive Robust Optimization](https://mlsanity.com/paper/2409.03731/) (2024)
- [Decision-calibrated prediction sets for robust power system operations](https://mlsanity.com/paper/2606.02081/) (2026)
- [Data-Driven Conditional Flexibility Index](https://mlsanity.com/paper/2601.16028/) (2026)
- [Generative Robust Optimisation](https://mlsanity.com/paper/2606.22536/) (2026)

## Abstract (arXiv)

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.