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

2026-05-14

AI Summary

Two-stage robust optimization under discrete uncertainty is notoriously challenging to solve due to the exponential number of scenarios, and existing scenario reduction methods often overlook problem-specific structure, limiting their effectiveness. This work proposes PRISE, a heuristic algorithm that constructs high-quality reduced scenario sets by evaluating the marginal impact of individual scenarios, and further introduces NeurPRISE, a neural surrogate model that dramatically accelerates the selection process. NeurPRISE is the first approach to integrate problem-driven scenario reduction with a neural surrogate, employing a hybrid architecture of graph neural networks and Transformers trained via imitation learning with a gain-aware ranking objective to efficiently learn scenario marginal gains and achieve zero-shot generalization. Experiments across three classes of two-stage robust optimization problems demonstrate that NeurPRISE achieves 7–200× speedups over PRISE while maintaining competitive regret performance and generalizing effectively to larger-scale instances and distribution-shifted scenarios.

Abstract

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.

Problem

• Two-Stage Robust Optimization
• Scenario Reduction
• Discrete Uncertainty
• Problem-Driven Selection
• Computational Tractability

Innovation

• scenario reduction
• two-stage robust optimization
• neural surrogate model
• GNN-Transformer
• imitation learning