# Deep Learning for Two-Stage Robust Integer Optimization

arXiv: https://arxiv.org/abs/2310.04345 · HTML: https://mlsanity.com/paper/2310.04345/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 82 references that are in the map.
- First posted on arXiv 6 Oct 2023.

## Builds on (most cited first, 28 of 28)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [Maximum Resilience of Artificial Neural Networks](https://mlsanity.com/paper/1705.01040/) (2017)
- [A Survey for Solving Mixed Integer Programming via Machine Learning](https://mlsanity.com/paper/2203.02878/) (2022)
- [When Deep Learning Meets Polyhedral Theory: A Survey](https://mlsanity.com/paper/2305.00241/) (2023)
- [ReLU Networks as Surrogate Models in Mixed-Integer Linear Programs](https://mlsanity.com/paper/1907.03140/) (2019)
- [Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch](https://mlsanity.com/paper/2112.13469/) (2021)
- [JANOS: An Integrated Predictive and Prescriptive Modeling Framework](https://mlsanity.com/paper/1911.09461/) (2019)
- [Learning Hard Optimization Problems: A Data Generation Perspective](https://mlsanity.com/paper/2106.02601/) (2021)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Neur2SP: Neural Two-Stage Stochastic Programming](https://mlsanity.com/paper/2205.12006/) (2022)
- [Neural Networks for Encoding Dynamic Security-Constrained Optimal Power Flow](https://mlsanity.com/paper/2003.07939/) (2020)
- [Robust Optimization using Machine Learning for Uncertainty Sets](https://mlsanity.com/paper/1407.1097/) (2014)
- [Optimizing Objective Functions from Trained ReLU Neural Networks via Sampling](https://mlsanity.com/paper/2205.14189/) (2022)
- [K-Adaptability in Two-Stage Mixed-Integer Robust Optimization](https://mlsanity.com/paper/1706.07097/) (2017)
- [Fast Continuous and Integer L-shaped Heuristics Through Supervised Learning](https://mlsanity.com/paper/2205.00897/) (2022)
- [Alternating mixed-integer programming and neural network training for approximating stochastic two-stage problems](https://mlsanity.com/paper/2305.06785/) (2023)
- [A data-driven robust optimization approach to scenario-based stochastic model predictive control](https://mlsanity.com/paper/1807.05146/) (2018)
- [Oracle-Based Algorithms for Binary Two-Stage Robust Optimization](https://mlsanity.com/paper/1905.05257/) (2019)
- [A Double-oracle, Logic-based Benders decomposition approach to solve the K-adaptability problem](https://mlsanity.com/paper/2209.02936/) (2022)
- [A Machine Learning Approach to Two-Stage Adaptive Robust Optimization](https://mlsanity.com/paper/2307.12409/) (2023)
- [A Lagrangian Dual Method for Two-Stage Robust Optimization with Binary Uncertainties](https://mlsanity.com/paper/2112.13138/) (2021)
- [An inexact column-and-constraint generation method to solve two-stage robust optimization problems](https://mlsanity.com/paper/2207.03291/) (2022)
- [Machine Learning for K-adaptability in Two-stage Robust Optimization](https://mlsanity.com/paper/2210.11152/) (2022)

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

- [Optimization Over Trained Neural Networks: Taking a Relaxing Walk](https://mlsanity.com/paper/2401.03451/) (2024)
- [Neur2BiLO: Neural Bilevel Optimization](https://mlsanity.com/paper/2402.02552/) (2024)

## Abstract (arXiv)

Robust optimization is an established framework for modeling optimization problems with uncertain parameters. While static robust optimization is often criticized for being too conservative, two-stage (or adjustable) robust optimization (2RO) provides a less conservative alternative by allowing some decisions to be made after the uncertain parameters have been revealed. Unfortunately, in the case of integer decision variables, existing solution methods for 2RO typically fail to solve large-scale instances, limiting the applicability of this modeling paradigm to simple cases. We propose Neur2RO, a deep-learning-augmented instantiation of the column-and-constraint-generation (CCG) algorithm, which expands the applicability of the 2RO framework to large-scale instances with integer decisions in both stages. A custom-designed neural network is trained to estimate the optimal value and feasibility of the second-stage problem. The network can be incorporated into CCG, leading to more computationally tractable subproblems in each of its iterations. The resulting algorithm enjoys approximation guarantees which depend on the neural network's prediction error. In our experiments, Neur2RO produces high-quality solutions quickly, outperforming state-of-the-art methods on two-stage knapsack, capital budgeting, and facility location problems. Compared to existing methods, which often run for hours, Neur2RO finds better solutions in a few seconds or minutes. Our code is available at https://github.com/khalil-research/Neur2RO.