Data-driven dynamic optimization with auxiliary covariates

Abstract

Optimization under uncertainty forms the foundation for many of the fundamental problems the operations research community seeks to solve. In this thesis, we develop and analyze algorithms that incorporate ideas from machine learning to optimize uncertain objectives directly from data. In the first chapter, we consider problems in which the decision affects the observed outcome, such as in personalized medicine and pricing. We present a framework for using observational data to learn to optimize an uncertain objective over a continuous and multi-dimensional decision space. Our approach accounts for the uncertainty in predictions, and we provide theoretical results that show this adds value. In addition, we test our approach on a Warfarin dosing example, and it outperforms the leading alternative methods.

In the second chapter, we develop an approach for solving dynamic optimization problems with covariates that uses machine learning to approximate the unknown stochastic process of the uncertainty. We provide theoretical guarantees on the effectiveness of our method and validate the guarantees with computational experiments. In the third chapter, we introduce a distributionally robust approach for incorporating covariates in large-scale, data-driven dynamic optimization. We prove that it is asymptotically optimal and provide a tractable general-purpose approximation scheme that scales to problems with many temporal stages. Across examples in shipment planning, inventory management, and finance, our method achieves improvements of up to 15% over alternatives. In the final chapter, we apply the techniques developed in previous chapters to the problem of optimizing the operating room schedule at a major US hospital.

Our partner institution faces significant census variability throughout the week, which limits the amount of patients it can accept due to resource constraints at peak times. We introduce a data-driven approach for this problem that combines machine learning with mixed integer optimization and demonstrate that it can reliably reduce the maximal weekly census.