Decision-focused predictions via pessimistic bilevel optimization: a computational study

• URL: http://arxiv.org/abs/2312.17640v2
• Date: Sun, 26 May 2024 09:36:07 GMT
• Title: Decision-focused predictions via pessimistic bilevel optimization: a computational study
• Authors: Víctor Bucarey, Sophia Calderón, Gonzalo Muñoz, Frederic Semet,
• Abstract summary: Uncertainty in optimization parameters is an important and longstanding challenge. We build predictive models that measure a emphregret measure on decisions taken with them. We show various computational techniques to achieve tractability.
• Score: 0.7499722271664147
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Dealing with uncertainty in optimization parameters is an important and longstanding challenge. Typically, uncertain parameters are predicted accurately, and then a deterministic optimization problem is solved. However, the decisions produced by this so-called \emph{predict-then-optimize} procedure can be highly sensitive to uncertain parameters. In this work, we contribute to recent efforts in producing \emph{decision-focused} predictions, i.e., to build predictive models that are constructed with the goal of minimizing a \emph{regret} measure on the decisions taken with them. We begin by formulating the exact expected regret minimization as a pessimistic bilevel optimization model. Then, we establish NP-completeness of this problem, even in a heavily restricted case. Using duality arguments, we reformulate it as a non-convex quadratic optimization problem. Finally, we show various computational techniques to achieve tractability. We report extensive computational results on shortest-path instances with uncertain cost vectors. Our results indicate that our approach can improve training performance over the approach of Elmachtoub and Grigas (2022), a state-of-the-art method for decision-focused learning.

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