Dynamic optimization with side information

TL;DR

This paper introduces a flexible, data-driven approach to dynamic optimization that leverages machine learning to incorporate side information, improving decision-making under uncertainty with proven asymptotic optimality and practical efficiency.

Contribution

It presents a novel framework combining machine learning with robust optimization, offering asymptotic optimality and a tractable approximation for multi-stage stochastic problems.

Findings

Achieves up to 15% improvement over alternatives.

Requires less than one minute for twelve-stage problems.

Demonstrates effectiveness across inventory, finance, and shipment planning.

Abstract

We develop a tractable and flexible approach for incorporating side information into dynamic optimization under uncertainty. The proposed framework uses predictive machine learning methods (such as $k$-nearest neighbors, kernel regression, and random forests) to weight the relative importance of various data-driven uncertainty sets in a robust optimization formulation. Through a novel measure concentration result for a class of 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 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.