# Neur2SP: Neural Two-Stage Stochastic Programming

arXiv: https://arxiv.org/abs/2205.12006 · HTML: https://mlsanity.com/paper/2205.12006/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 20 May 2022.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [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)
- [OMLT: Optimization & Machine Learning Toolkit](https://mlsanity.com/paper/2202.02414/) (2022)
- [ReLU Networks as Surrogate Models in Mixed-Integer Linear Programs](https://mlsanity.com/paper/1907.03140/) (2019)
- [JANOS: An Integrated Predictive and Prescriptive Modeling Framework](https://mlsanity.com/paper/1911.09461/) (2019)
- [Improved Adversarial Training via Learned Optimizer](https://mlsanity.com/paper/2004.12227/) (2020)
- [Learning to Defend by Learning to Attack](https://mlsanity.com/paper/1811.01213/) (2018)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Neural Networks for Encoding Dynamic Security-Constrained Optimal Power Flow](https://mlsanity.com/paper/2003.07939/) (2020)
- [A learning-based algorithm to quickly compute good primal solutions for Stochastic Integer Programs](https://mlsanity.com/paper/1912.08112/) (2019)
- [Problem-Driven Scenario Clustering in Stochastic Optimization](https://mlsanity.com/paper/2106.11717/) (2021)
- [Neural Stochastic Dual Dynamic Programming](https://mlsanity.com/paper/2112.00874/) (2021)
- [Fast Continuous and Integer L-shaped Heuristics Through Supervised Learning](https://mlsanity.com/paper/2205.00897/) (2022)
- [Learning for Robust Combinatorial Optimization: Algorithm and Application](https://mlsanity.com/paper/2112.10377/) (2021)

## Built on by (most cited first, 17 of 17)

- [When Deep Learning Meets Polyhedral Theory: A Survey](https://mlsanity.com/paper/2305.00241/) (2023)
- [Optimization Over Trained Neural Networks: Taking a Relaxing Walk](https://mlsanity.com/paper/2401.03451/) (2024)
- [Graph Reinforcement Learning for Network Control via Bi-Level Optimization](https://mlsanity.com/paper/2305.09129/) (2023)
- [Reinforcement learning with combinatorial actions for coupled restless bandits](https://mlsanity.com/paper/2503.01919/) (2025)
- [Neur2BiLO: Neural Bilevel Optimization](https://mlsanity.com/paper/2402.02552/) (2024)
- [Deep Learning for Two-Stage Robust Integer Optimization](https://mlsanity.com/paper/2310.04345/) (2023)
- [HGCN2SP: Hierarchical Graph Convolutional Network for Two-Stage Stochastic Programming](https://mlsanity.com/paper/2511.16027/) (2025)
- [Relaxation-Informed Training of Neural Network Surrogate Models](https://mlsanity.com/paper/2604.22746/) (2026)
- [Latency-Aware Bid Acceptance under Operational Feasibility: A Public Benchmark with Hindsight Ceilings](https://mlsanity.com/paper/2607.07343/) (2026)
- [Contextual Scenario Generation for Two-Stage Stochastic Programming](https://mlsanity.com/paper/2502.05349/) (2025)
- [Neural Two-Stage Stochastic Optimization for Solving Unit Commitment Problem](https://mlsanity.com/paper/2507.09503/) (2025)
- [Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision](https://mlsanity.com/paper/2603.04431/) (2026)
- [Scalable Solution of the Stochastic Multi-path Traveling Salesman Problem via Neural Networks](https://mlsanity.com/paper/2605.14662/) (2026)
- [Diff2SP: Diffusion Models for Correlated Scenario Generation in Stochastic Programming](https://mlsanity.com/paper/2606.05649/) (2026)
- [Learning Optimization Proxies for Sequential Contextual Stochastic Programs: An Order Fulfillment Application](https://mlsanity.com/paper/2606.25362/) (2026)
- [DCEmbed: Scalable Optimization over Neural Surrogates](https://mlsanity.com/paper/2609.33879/) (2026)
- [Optimization for One, Feasibility for Most: Decoupling Optimization from Feasibility in Chance-Constrained Programs](https://mlsanity.com/paper/2610.19027/) (2026)

## Abstract (arXiv)

Stochastic Programming is a powerful modeling framework for decision-making under uncertainty. In this work, we tackle two-stage stochastic programs (2SPs), the most widely used class of stochastic programming models. Solving 2SPs exactly requires optimizing over an expected value function that is computationally intractable. Having a mixed-integer linear program (MIP) or a nonlinear program (NLP) in the second stage further aggravates the intractability, even when specialized algorithms that exploit problem structure are employed. Finding high-quality (first-stage) solutions -- without leveraging problem structure -- can be crucial in such settings. We develop Neur2SP, a new method that approximates the expected value function via a neural network to obtain a surrogate model that can be solved more efficiently than the traditional extensive formulation approach. Neur2SP makes no assumptions about the problem structure, in particular about the second-stage problem, and can be implemented using an off-the-shelf MIP solver. Our extensive computational experiments on four benchmark 2SP problem classes with different structures (containing MIP and NLP second-stage problems) demonstrate the efficiency (time) and efficacy (solution quality) of Neur2SP. In under 1.66 seconds, Neur2SP finds high-quality solutions across all problems even as the number of scenarios increases, an ideal property that is difficult to have for traditional 2SP solution techniques. Namely, the most generic baseline method typically requires minutes to hours to find solutions of comparable quality.