# A Machine Learning Approach to Two-Stage Adaptive Robust Optimization

arXiv: https://arxiv.org/abs/2307.12409 · HTML: https://mlsanity.com/paper/2307.12409/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 37 references that are in the map.
- First posted on arXiv 23 Jul 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Online Mixed-Integer Optimization in Milliseconds](https://mlsanity.com/paper/1907.02206/) (2019)
- [The Voice of Optimization](https://mlsanity.com/paper/1812.09991/) (2018)
- [Optimal Policy Trees](https://mlsanity.com/paper/2012.02279/) (2020)
- [CoCo: Online Mixed-Integer Control via Supervised Learning](https://mlsanity.com/paper/2107.08143/) (2021)
- [Learning to Optimize Computational Resources: Frugal Training with Generalization Guarantees](https://mlsanity.com/paper/1905.10819/) (2019)
- [Optimal Scenario Reduction for One- and Two-Stage Robust Optimization](https://mlsanity.com/paper/2209.00499/) (2022)
- [Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind](https://mlsanity.com/paper/1409.2936/) (2014)
- [An adaptive robust optimization model for parallel machine scheduling](https://mlsanity.com/paper/2102.08677/) (2021)

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

- [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)
- [Learning Scenario Reduction for Two-Stage Robust Optimization with Discrete Uncertainty](https://mlsanity.com/paper/2605.14494/) (2026)

## Abstract (arXiv)

We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the optimal wait-and-see decisions into what we denote as the strategy. We solve multiple similar ARO instances in advance using the column and constraint generation algorithm and extract the optimal strategies to generate a training set. We train machine learning models that predict high-quality strategies for the here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the wait-and-see decisions. The models can be applied to problems with varying dimensions. We also introduce novel methods to expedite training data generation and reduce the number of different target classes the machine learning algorithm needs to be trained on. We apply the proposed approach to the facility location, the multi-item inventory control and the unit commitment problems. Our approach solves ARO problems drastically faster than the state-of-the-art algorithms with high accuracy.