# HGCN2SP: Hierarchical Graph Convolutional Network for Two-Stage Stochastic Programming

arXiv: https://arxiv.org/abs/2511.16027 · HTML: https://mlsanity.com/paper/2511.16027/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 20 Nov 2025.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022)
- [On Representing Mixed-Integer Linear Programs by Graph Neural Networks](https://mlsanity.com/paper/2210.10759/) (2022)
- [Neur2SP: Neural Two-Stage Stochastic Programming](https://mlsanity.com/paper/2205.12006/) (2022)
- [A learning-based algorithm to quickly compute good primal solutions for Stochastic Integer Programs](https://mlsanity.com/paper/1912.08112/) (2019)
- [Learning to Reformulate for Linear Programming](https://mlsanity.com/paper/2201.06216/) (2022)
- [Problem-Driven Scenario Clustering in Stochastic Optimization](https://mlsanity.com/paper/2106.11717/) (2021)
- [Fast Continuous and Integer L-shaped Heuristics Through Supervised Learning](https://mlsanity.com/paper/2205.00897/) (2022)
- [Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure](https://mlsanity.com/paper/1511.03074/) (2015)
- [Scenario Reduction Revisited: Fundamental Limits and Guarantees](https://mlsanity.com/paper/1701.04072/) (2017)
- [On the Convergence of L-shaped Algorithms for Two-Stage Stochastic Programming](https://mlsanity.com/paper/2309.01244/) (2023)

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

- [Learning Scenario Reduction for Two-Stage Robust Optimization with Discrete Uncertainty](https://mlsanity.com/paper/2605.14494/) (2026)
- [Diff2SP: Diffusion Models for Correlated Scenario Generation in Stochastic Programming](https://mlsanity.com/paper/2606.05649/) (2026)

## Abstract (arXiv)

Two-stage Stochastic Programming (2SP) is a standard framework for modeling decision-making problems under uncertainty. While numerous methods exist, solving such problems with many scenarios remains challenging. Selecting representative scenarios is a practical method for accelerating solutions. However, current approaches typically rely on clustering or Monte Carlo sampling, failing to integrate scenario information deeply and overlooking the significant impact of the scenario order on solving time. To address these issues, we develop HGCN2SP, a novel model with a hierarchical graph designed for 2SP problems, encoding each scenario and modeling their relationships hierarchically. The model is trained in a reinforcement learning paradigm to utilize the feedback of the solver. The policy network is equipped with a hierarchical graph convolutional network for feature encoding and an attention-based decoder for scenario selection in proper order. Evaluation of two classic 2SP problems demonstrates that HGCN2SP provides high-quality decisions in a short computational time. Furthermore, HGCN2SP exhibits remarkable generalization capabilities in handling large-scale instances, even with a substantial number of variables or scenarios that were unseen during the training phase.