Robust Data-driven Prescriptiveness Optimization
Mehran Poursoltani Erick Delage Angelos Georghiou
The abundance of data has led to the emergence of a variety of optimization
techniques that attempt to leverage available side information to provide more
anticipative decisions. The wide range of methods and contexts of application
have motivated the design of a universal unitless measure of performance known
as the coefficient of prescriptiveness. This coefficient was designed to
quantify both the quality of contextual decisions compared to a reference one
and the prescriptive power of side information. To identify policies that
maximize the former in a data-driven context, this paper introduces a
distributionally robust contextual optimization model where the coefficient of
prescriptiveness substitutes for the classical empirical risk minimization
objective. We present a bisection algorithm to solve this model, which relies
on solving a series of linear programs when the distributional ambiguity set
has an appropriate nested form and polyhedral structure. Studying a contextual
shortest path problem, we evaluate the robustness of the resulting policies
against alternative methods when the out-of-sample dataset is subject to
varying amounts of distribution shift.