From Predictions to Prescriptions in Multistage Optimization Problems

TL;DR

This paper presents a machine learning-based framework for solving multistage optimization problems under uncertainty, leveraging auxiliary data and predictive methods to improve decision-making and demonstrate practical benefits.

Contribution

It introduces a novel approach combining ML predictive techniques with multistage optimization, providing asymptotic and finite-sample optimality guarantees.

Findings

Significant cost reduction by incorporating auxiliary data.

Methods are asymptotically optimal under mild conditions.

Finite sample guarantees established for kNN-based solutions.

Abstract

In this paper, we introduce a framework for solving finite-horizon multistage optimization problems under uncertainty in the presence of auxiliary data. We assume the joint distribution of the uncertain quantities is unknown, but noisy observations, along with observations of auxiliary covariates, are available. We utilize effective predictive methods from machine learning (ML), including $k$-nearest neighbors regression ($k$NN), classification and regression trees (CART), and random forests (RF), to develop specific methods that are applicable to a wide variety of problems. We demonstrate that our solution methods are asymptotically optimal under mild conditions. Additionally, we establish finite sample guarantees for the optimality of our method with $k$NN weight functions. Finally, we demonstrate the practicality of our approach with computational examples. We see a significant decrease in cost by taking into account the auxiliary data in the multistage setting.