Dynamic optimization with side information

We develop a tractable and flexible data-driven approach for incorporating side information into multi-stage stochastic programming. The proposed framework uses predictive machine learning methods (such as k-nearest neighbors, kernel regression, and random forests) to weight the relative importance of vari-ous data-driven uncertainty sets in a robust optimization formulation. Through a novel measure concen-tration result for a class of supervised machine learning methods, we prove that the proposed approach is asymptotically optimal for multi-period stochastic programming with side information. We also describe a general-purpose approximation for these optimization problems, based on overlapping linear decision rules, which is computationally tractable and produces high-quality solutions for dynamic problems with many stages. Across a variety of multi-stage and single-stage examples in inventory management, finance, and shipment planning, our method achieves improvements of up to 15% over alternatives and requires less than one minute of computation time on problems with twelve stages.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This article presents a data-driven approach that incorporates side information into multi-stage stochastic programming using predictive machine learning methods. The proposed method achieves asymptotic optimality for multi-period stochastic programming with side information, and introduces a general-purpose approximation for dynamic problems that produces high-quality solutions.