From Predictions to Prescriptions in Multistage Optimization Problems
This work addresses optimization problems in uncertain environments for fields like operations research, offering a novel framework that integrates predictive ML methods to improve decision-making.
The paper tackles multistage optimization under uncertainty by using machine learning methods like kNN and random forests to incorporate auxiliary data, showing asymptotic optimality and finite sample guarantees, with computational examples demonstrating significant cost reductions.
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.