Contextual Scenario Generation for Two-Stage Stochastic Programming
This work addresses computational efficiency for decision-makers in stochastic optimization, though it appears incremental by building on existing scenario generation approaches.
The paper tackles the challenge of generating a small set of surrogate scenarios for two-stage stochastic programming to reduce computational barriers, proposing contextual scenario generation methods that leverage contextual information and achieve high-quality decisions with reduced scenario counts.
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.