Dynamic optimization with side information

Dimitris Bertsimas, Christopher McCord and Bradley Sturt

European Journal of Operational Research, 2023, vol. 304, issue 2, 634-651

Abstract: 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 various data-driven uncertainty sets in a robust optimization formulation. Through a novel measure concentration 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.

Keywords: Stochastic programming; Distributionally robust optimization; Machine learning; Dynamic optimization (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:304:y:2023:i:2:p:634-651

DOI: 10.1016/j.ejor.2022.03.030

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