Dynamic optimization with side information
This work addresses dynamic optimization problems with side information for domains such as inventory management and finance, offering a tractable and asymptotically optimal approach that is incremental in combining existing methods.
The paper tackles dynamic optimization under uncertainty by incorporating side information using predictive machine learning methods to weight data-driven uncertainty sets in a robust optimization framework, achieving up to 15% improvements over alternatives in examples like inventory management and finance with less than one minute of computation time for twelve-stage problems.
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.