# Robust Optimization using Machine Learning for Uncertainty Sets

arXiv: https://arxiv.org/abs/1407.1097 · HTML: https://mlsanity.com/paper/1407.1097/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2014.

## Built on by (most cited first, 14 of 14)

- [Exploring the Whole Rashomon Set of Sparse Decision Trees](https://mlsanity.com/paper/2209.08040/) (2022)
- [A Path to Simpler Models Starts With Noise](https://mlsanity.com/paper/2310.19726/) (2023)
- [Exploring and Interacting with the Set of Good Sparse Generalized Additive Models](https://mlsanity.com/paper/2303.16047/) (2023)
- [The Rashomon Importance Distribution: Getting RID of Unstable, Single Model-based Variable Importance](https://mlsanity.com/paper/2309.13775/) (2023)
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- [A Survey on the Robustness of Computer Vision Models against Common Corruptions](https://mlsanity.com/paper/2305.06024/) (2023)
- [Systemizing Multiplicity: The Curious Case of Arbitrariness in Machine Learning](https://mlsanity.com/paper/2501.14959/) (2025)
- [Exploration of the Rashomon Set Assists Trustworthy Explanations for Medical Data](https://mlsanity.com/paper/2308.11446/) (2023)
- [Differentially Private Sampling from Rashomon Sets, and the Universality of Langevin Diffusion for Convex Optimization](https://mlsanity.com/paper/2204.01585/) (2022)
- [Deep Learning for Two-Stage Robust Integer Optimization](https://mlsanity.com/paper/2310.04345/) (2023)
- [A Deep Generative Learning Approach for Two-stage Adaptive Robust Optimization](https://mlsanity.com/paper/2409.03731/) (2024)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Everywhere Learning: Artificial Intelligence with Pointwise Constraints](https://mlsanity.com/paper/2606.01557/) (2026)
- [Learning Relevant Contextual Variables Within Bayesian Optimization](https://mlsanity.com/paper/2305.14120/) (2023)

## Abstract (arXiv)

Our goal is to build robust optimization problems for making decisions based on complex data from the past. In robust optimization (RO) generally, the goal is to create a policy for decision-making that is robust to our uncertainty about the future. In particular, we want our policy to best handle the the worst possible situation that could arise, out of an uncertainty set of possible situations. Classically, the uncertainty set is simply chosen by the user, or it might be estimated in overly simplistic ways with strong assumptions; whereas in this work, we learn the uncertainty set from data collected in the past. The past data are drawn randomly from an (unknown) possibly complicated high-dimensional distribution. We propose a new uncertainty set design and show how tools from statistical learning theory can be employed to provide probabilistic guarantees on the robustness of the policy.