Contextual Scenario Generation for Two-Stage Stochastic Programming

TL;DR

This paper introduces a novel method for generating a small, high-quality set of surrogate scenarios for two-stage stochastic programming by leveraging contextual information and neural architectures, improving decision-making efficiency.

Contribution

It proposes two new approaches—distributional and task-based—for contextual scenario generation that effectively incorporate context and optimize decision quality.

Findings

The methods produce high-quality surrogate scenarios with fewer samples.

Numerical experiments show improved decision accuracy and computational efficiency.

Approaches are applicable to various problem structures.

Abstract

Two-stage stochastic programs (2SPs) are important tools for making decisions under uncertainty. Decision-makers use contextual information to generate a set of scenarios to represent the true conditional distribution. However, the number of scenarios required is a barrier to implementing 2SPs, motivating the problem of generating a small set of surrogate scenarios that yield high-quality decisions when they represent uncertainty. Current scenario generation approaches do not leverage contextual information or do not address computational concerns. In response, we propose contextual scenario generation (CSG) to learn a mapping between the context and a set of surrogate scenarios of user-specified size. First, we propose a distributional approach that learns the mapping by minimizing a distributional distance between the predicted surrogate scenarios and the true contextual distribution. Second, we propose a task-based approach that aims to produce surrogate scenarios that yield high-quality decisions. The task-based approach uses neural architectures to approximate the downstream objective and leverages the approximation to search for the mapping. The proposed approaches apply to various problem structures and loosely only require efficient solving of the associated subproblems and 2SPs defined on the reduced scenario sets. Numerical experiments demonstrating the effectiveness of the proposed methods are presented.