Data-Driven Robust Optimization

TL;DR

This paper introduces a flexible, data-driven method for constructing uncertainty sets in robust optimization using statistical hypothesis tests, providing strong probabilistic guarantees and improved performance over traditional methods.

Contribution

It presents a novel schema for designing uncertainty sets from data that are computationally tractable and applicable across various problems, with proven probabilistic guarantees.

Findings

Data-driven sets outperform traditional robust optimization techniques.

The approach is computationally tractable and widely applicable.

Strong finite-sample probabilistic guarantees are provided.

Abstract

The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee. \edit{We describe concrete procedures for choosing an appropriate set for a given application and applying our approach to multiple uncertain constraints. Computational evidence in portfolio management and queuing confirm that our data-driven sets significantly outperform traditional robust optimization techniques whenever data is available.