Scenario trees and policy selection for multistage stochastic programming using machine learning

TL;DR

This paper introduces a hybrid approach combining scenario trees and machine learning to improve policy selection and solution quality in multistage stochastic programming, enabling efficient out-of-sample evaluation.

Contribution

It presents a novel hybrid algorithm that uses machine learning to select the best scenario tree for multistage stochastic problems, enhancing solution quality and computational efficiency.

Findings

Effective trade-offs between run times and solution quality.

Parallel solution of multiple scenario trees improves policy selection.

Machine learning-based simulation aids in out-of-sample evaluation.

Abstract

We propose a hybrid algorithmic strategy for complex stochastic optimization problems, which combines the use of scenario trees from multistage stochastic programming with machine learning techniques for learning a policy in the form of a statistical model, in the context of constrained vector-valued decisions. Such a policy allows one to run out-of-sample simulations over a large number of independent scenarios, and obtain a signal on the quality of the approximation scheme used to solve the multistage stochastic program. We propose to apply this fast simulation technique to choose the best tree from a set of scenario trees. A solution scheme is introduced, where several scenario trees with random branching structure are solved in parallel, and where the tree from which the best policy for the true problem could be learned is ultimately retained. Numerical tests show that excellent trade-offs can be achieved between run times and solution quality.