Fantastic Out-Of-Sample Optimality and Where to Find Them in Data-Driven Optimization.
In data-driven optimization, the decision-maker is not privy to the true distribution, but possesses a historical data set. We consider the context where the decision-maker also has knowledge that it lies in some hypothesis set. We define a prescriptive solution as a decision rule mapping data sets to decisions. In general, there does not exist solutions generalizable over the hypothesis set. Hence, we define out-of-sample optimality as a local average of some neighbourhood in the hypothesis set and over the sampling distribution. We prove sufficient conditions for local out-of-sample optimality and propose an optimization problem that solves efficiently for such an out-of-sample optimal solution. When applied on the newsvendor model, our solution has strong performance against alternatives in the literature. We also discuss potential implications of our research on end-to-end learning and Bayesian inference.
About: Gar Goei Loke is an assistant professor at Rotterdam School of Management at Erasmus University Rotterdam. His research interests are in the area of Robust Optimization, especially in applying robust optimization to problems in service management or queueing networks. He also works on the interface between Machine Learning and Operations Research, such as contextual stochastic optimization.