# Learning Scenario Reduction for Two-Stage Robust Optimization with Discrete Uncertainty

arXiv: https://arxiv.org/abs/2605.14494 · HTML: https://mlsanity.com/paper/2605.14494/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [K-Adaptability in Two-Stage Mixed-Integer Robust Optimization](https://mlsanity.com/paper/1706.07097/) (2017)
- [Problem-Driven Scenario Clustering in Stochastic Optimization](https://mlsanity.com/paper/2106.11717/) (2021)
- [Optimal Scenario Reduction for One- and Two-Stage Robust Optimization](https://mlsanity.com/paper/2209.00499/) (2022)
- [A Machine Learning Approach to Two-Stage Adaptive Robust Optimization](https://mlsanity.com/paper/2307.12409/) (2023)
- [Data-driven Prediction of Relevant Scenarios for Robust Combinatorial Optimization](https://mlsanity.com/paper/2203.16642/) (2022)
- [A Deep Generative Learning Approach for Two-stage Adaptive Robust Optimization](https://mlsanity.com/paper/2409.03731/) (2024)
- [HGCN2SP: Hierarchical Graph Convolutional Network for Two-Stage Stochastic Programming](https://mlsanity.com/paper/2511.16027/) (2025)
- [Problem-Driven Scenario Reduction and Scenario Approximation for Robust Optimization](https://mlsanity.com/paper/2410.08863/) (2024)

## Abstract (arXiv)

Two-Stage Robust Optimization (2RO) with discrete uncertainty is challenging, often rendering exact solutions prohibitive. Scenario reduction alleviates this issue by selecting a small, representative subset of scenarios to enable tractable computation. However, existing methods are largely problem-agnostic, operating solely on the uncertainty set without consulting the feasible region or recourse structure. In this paper, we introduce PRISE, a problem-driven sequential lookahead heuristic that constructs reduced scenario sets by evaluating the marginal impact of each scenario. While PRISE yields high-quality scenario subsets, each selection step requires solving multiple subproblems, making it computationally expensive at scale. To address this, we propose NeurPRISE, a neural surrogate model built on a GNN-Transformer backbone that encodes the per-scenario structure via graph convolution and captures cross-scenario interactions through attention. NeurPRISE is trained via imitation learning with a gain-aware ranking objective, which distills marginal gain information from PRISE into a learned scoring function for scenario ranking and selection. Extensive results on three 2RO problems show that NeurPRISE consistently achieves competitive regret relative to comprehensive methods, maintains strong calability with varying numbers of scenarios, and delivers 7-200x speedup over PRISE. NeurPRISE also exhibits strong zero-shot generalization, effectively handling instances with larger problem scales (up to 5x), more scenarios (up to 4x), and distribution shifts.