# Optimal Scenario Reduction for One- and Two-Stage Robust Optimization

arXiv: https://arxiv.org/abs/2209.00499 · HTML: https://mlsanity.com/paper/2209.00499/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2022.

## Built on by (most cited first, 3 of 3)

- [A Machine Learning Approach to Two-Stage Adaptive Robust Optimization](https://mlsanity.com/paper/2307.12409/) (2023)
- [Learning Scenario Reduction for Two-Stage Robust Optimization with Discrete Uncertainty](https://mlsanity.com/paper/2605.14494/) (2026)
- [Which Directions Matter? Sparse Design for Affine Robust Optimization](https://mlsanity.com/paper/2606.14648/) (2026)

## Abstract (arXiv)

Robust optimization typically follows a worst-case perspective, where a single scenario may determine the objective value of a given solution. Accordingly, it is a challenging task to reduce the size of an uncertainty set without changing the resulting objective value too much. On the other hand, robust optimization problems with many scenarios tend to be hard to solve, in particular for two-stage problems. Hence, a reduced uncertainty set may be central to find solutions in reasonable time. We propose scenario reduction methods that give guarantees on the performance of the resulting robust solution. Scenario reduction problems for one- and two-stage robust optimization are framed as optimization problems that only depend on the uncertainty set and not on the underlying decision making problem. Experimental results indicate that objective values for the reduced uncertainty sets are closely correlated to original objective values, resulting in better solutions than when using general-purpose clustering methods such as K-means.