# ICNN-enhanced 2SP: Leveraging input convex neural networks for solving two-stage stochastic programming

arXiv: https://arxiv.org/abs/2505.05261 · HTML: https://mlsanity.com/paper/2505.05261/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 47 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 15 of 15)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [OR-Gym: A Reinforcement Learning Library for Operations Research Problems](https://mlsanity.com/paper/2008.06319/) (2020)
- [Learning in structured MDPs with convex cost functions: Improved regret bounds for inventory management](https://mlsanity.com/paper/1905.04337/) (2019)
- [Input Convex Neural Networks for Building MPC](https://mlsanity.com/paper/2011.13227/) (2020)
- [A learning-based algorithm to quickly compute good primal solutions for Stochastic Integer Programs](https://mlsanity.com/paper/1912.08112/) (2019)
- [P-split formulations: A class of intermediate formulations between big-M and convex hull for disjunctive constraints](https://mlsanity.com/paper/2202.05198/) (2022)
- [Learning Optimal Power Flow Value Functions with Input-Convex Neural Networks](https://mlsanity.com/paper/2310.04605/) (2023)
- [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)
- [Alternating mixed-integer programming and neural network training for approximating stochastic two-stage problems](https://mlsanity.com/paper/2305.06785/) (2023)
- [Portfolio Construction with Gaussian Mixture Returns and Exponential Utility via Convex Optimization](https://mlsanity.com/paper/2205.04563/) (2022)
- [Fast Explicit Machine Learning-Based Model Predictive Control of Nonlinear Processes Using Input Convex Neural Networks](https://mlsanity.com/paper/2408.06580/) (2024)
- [Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems](https://mlsanity.com/paper/2410.09166/) (2024)

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

- [Relaxation-Informed Training of Neural Network Surrogate Models](https://mlsanity.com/paper/2604.22746/) (2026)
- [SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functions](https://mlsanity.com/paper/2604.22355/) (2026)
- [Input convex neural networks as surrogates in mathematical optimisation](https://mlsanity.com/paper/2608.09707/) (2026)

## Abstract (arXiv)

Two-stage stochastic programming (2SP) offers a basic framework for modelling decision-making under uncertainty, yet scalability remains a challenge due to the computational complexity of recourse function evaluation. Existing learning-based methods like Neural Two-Stage Stochastic Programming (Neur2SP) employ neural networks (NNs) as recourse function surrogates but rely on computationally intensive mixed-integer programming (MIP) formulations. We propose ICNN-enhanced 2SP, a method that leverages Input Convex Neural Networks (ICNNs) to exploit linear programming (LP) representability in convex 2SP problems. By architecturally enforcing convexity and enabling exact inference through LP, our approach eliminates the need for integer variables inherent in the conventional MIP-based formulation while retaining an exact embedding of the ICNN surrogate within the 2SP framework. This results in a more computationally efficient alternative, and we show that good solution quality can be maintained. Comprehensive experiments reveal that ICNNs incur only marginally longer training times while achieving validation accuracy on par with their standard NN counterparts. Across benchmark problems, ICNN-enhanced 2SP often exhibits considerably faster solution times than the MIP-based formulations while preserving solution quality, with these advantages becoming significantly more pronounced as problem scale increases. For the most challenging instances, the method achieves speedups of up to 100× with solution quality superior to MIP-based formulations.