# Machine Learning for K-adaptability in Two-stage Robust Optimization

arXiv: https://arxiv.org/abs/2210.11152 · HTML: https://mlsanity.com/paper/2210.11152/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 20 Oct 2022.

## Builds on (most cited first, 6 of 6)

- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Monte Carlo Tree Search: A Review of Recent Modifications and Applications](https://mlsanity.com/paper/2103.04931/) (2021)
- [MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers](https://mlsanity.com/paper/2205.14210/) (2022)
- [Finding Backdoors to Integer Programs: A Monte Carlo Tree Search Framework](https://mlsanity.com/paper/2110.08423/) (2021)
- [K-Adaptability in Two-Stage Mixed-Integer Robust Optimization](https://mlsanity.com/paper/1706.07097/) (2017)
- [A Double-oracle, Logic-based Benders decomposition approach to solve the K-adaptability problem](https://mlsanity.com/paper/2209.02936/) (2022)

## Built on by (most cited first, 2 of 2)

- [Deep Learning for Two-Stage Robust Integer Optimization](https://mlsanity.com/paper/2310.04345/) (2023)
- [Imitation Learning for Combinatorial Optimisation under Uncertainty](https://mlsanity.com/paper/2601.05383/) (2026)

## Abstract (arXiv)

Two-stage robust optimization problems constitute one of the hardest optimization problem classes. One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the uncertainty set of scenarios into K subsets, and optimizes decisions corresponding to each of these subsets. In general case, it is solved using the K-adaptability branch-and-bound algorithm, which requires exploration of exponentially-growing solution trees. To accelerate finding high-quality solutions in such trees, we propose a machine learning-based node selection strategy. In particular, we construct a feature engineering scheme based on general two-stage robust optimization insights that allows us to train our machine learning tool on a database of resolved B&B trees, and to apply it as-is to problems of different sizes and/or types. We experimentally show that using our learned node selection strategy outperforms a vanilla, random node selection strategy when tested on problems of the same type as the training problems, also in case the K-value or the problem size differs from the training ones.