2019/07/17 by Dimitris Bertsimas, Bertsimas, Dimitris, Christopher McCord +3 · 3 citations
Business, Management and Accounting · Computer Science · Decision Sciences · Mathematics · #Forecasting Techniques and Applications #Risk and Portfolio Optimization #Supply Chain and Inventory Management #cs.LG #math.OC #stat.ML
paper · pdf · doi:10.48550/arxiv.1907.07307
arxiv created 2020/07/21 · arxiv updated 2020/07/23
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.