A bilevel framework for decision-making under uncertainty with contextual information

TL;DR

This paper introduces a bilevel optimization framework for decision-making under uncertainty that leverages contextual information to improve decision quality, demonstrated through practical and case study applications.

Contribution

It presents a novel bilevel modeling approach that integrates decision-guided prediction with regularization and reformulation techniques for efficient solution.

Findings

Decision-guided models outperform traditional statistical models in practical problems.

The approach is computationally feasible with off-the-shelf solvers.

In a case study, the method benefits a power producer under specific cost and capacity conditions.

Abstract

In this paper, we propose a novel approach for data-driven decision-making under uncertainty in the presence of contextual information. Given a finite collection of observations of the uncertain parameters and potential explanatory variables (i.e., the contextual information), our approach fits a parametric model to those data that is specifically tailored to maximizing the decision value, while accounting for possible feasibility constraints. From a mathematical point of view, our framework translates into a bilevel program, for which we provide both a fast regularization procedure and a big-M-based reformulation that can be solved using off-the-shelf optimization solvers. We showcase the benefits of moving from the traditional scheme for model estimation (based on statistical quality metrics) to decision-guided prediction using three different practical problems. We also compare our approach with existing ones in a realistic case study that considers a strategic power producer that participates in the Iberian electricity market. Finally, we use these numerical simulations to analyze the conditions (in terms of the firm's cost structure and production capacity) under which our approach proves to be more advantageous to the producer.