Optimize-via-Predict: Realizing out-of-sample optimality in data-driven optimization

TL;DR

This paper introduces a data-driven optimization framework that achieves out-of-sample optimality by leveraging local hypothesis neighborhoods, combining statistical theory with efficient algorithms, and demonstrating strong results on the newsvendor problem.

Contribution

It develops a novel approach for out-of-sample optimality in data-driven optimization using local hypothesis neighborhoods and efficient sampling algorithms.

Findings

Strong performance on the newsvendor model

Efficient solution via sampling and bisection search

Potential applications in learning and Bayesian optimization

Abstract

We examine a stochastic formulation for data-driven optimization wherein the decision-maker is not privy to the true distribution, but has knowledge that it lies in some hypothesis set and possesses a historical data set, from which information about it can be gleaned. We define a prescriptive solution as a decision rule mapping such a data set to decisions. As there does not exist prescriptive solutions that are generalizable over the entire hypothesis set, we define out-of-sample optimality as a local average over a neighbourhood of hypotheses, and averaged over the sampling distribution. We prove sufficient conditions for local out-of-sample optimality, which reduces to functions of the sufficient statistic of the hypothesis family. We present an optimization problem that would solve for such an out-of-sample optimal solution, and does so efficiently by a combination of sampling and bisection search algorithms. Finally, we illustrate our model on the newsvendor model, and find strong performance when compared against alternatives in the literature. There are potential implications of our research on end-to-end learning and Bayesian optimization.