Robust Data-driven Prescriptiveness Optimization

Mehran Poursoltani; Erick Delage; Angelos Georghiou

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arXiv · 2306.05937

Robust Data-driven Prescriptiveness Optimization

Mehran Poursoltani·Erick Delage·Angelos Georghiou

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Abstract

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.

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Mehran Poursoltani, Erick Delage, Angelos Georghiou. 2023-06-09. Robust Data-driven Prescriptiveness Optimization. https://arxiv.org/abs/2306.05937

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