Robust Data-driven Prescriptiveness Optimization

• URL: http://arxiv.org/abs/2306.05937v2
• Date: Mon, 3 Jun 2024 19:55:35 GMT
• Title: Robust Data-driven Prescriptiveness Optimization
• Authors: Mehran Poursoltani, Erick Delage, Angelos Georghiou,
• Abstract summary: This paper introduces a distributionally robust contextual optimization model where the coefficient of prescriptiveness substitutes for the classical empirical risk objective minimization. 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.
• Score: 4.792851066169871
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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