Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach
We consider generic stochastic optimization problems in the presence of side information that enables a more insightful decision. The side information constitutes observable exogenous covariates that alter the conditional probability distribution of the random problem parameters. Decision-makers who adapt their decisions according to the observed side information solve a stochastic optimization problem where the objective function is specified by the conditional expectation of the random cost. If the joint probability distribution is unknown, then the conditional expectation can be approximated in a data-driven manner using the Nadaraya-Watson kernel regression. While the emerging approximation scheme has found successful applications in diverse decision problems under uncertainty, it is largely unknown whether the scheme can provide any reasonable out-of-sample performance guarantees. In this talk, we establish guarantees for the generic problems by leveraging techniques from moderate deviations theory. Our analysis motivates the use of a variance-based regularization scheme which, in general, leads to a non-convex optimization problem. We adopt ideas from distributionally robust optimization to obtain tractable formulations. We present numerical experiments for inventory management and wind energy commitment problems to highlight the effectiveness of our regularization scheme.
Grani A. Hanasusanto is an Assistant Professor of Operations Research and Industrial Engineering at The University of Texas at Austin (UT). Before joining UT, he was a postdoctoral researcher at the College of Management of Technology at École Polytechnique Fédérale de Lausanne. He holds a PhD degree in Operations Research from Imperial College London and an MSc degree in Financial Engineering from the National University of Singapore. He is the recipient of the 2018 NSF CAREER Award. His research focuses on the design and analysis of tractable solution schemes for decision-making problems under uncertainty, with applications in operations management, energy systems, finance, machine learning and data analytics.