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Pré-Publication, Document De Travail Année : 2023

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

Résumé

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 formulate the exact expected regret minimization as a pessimistic bilevel optimization model. Then, 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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hal-04397536 , version 1 (16-01-2024)

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Víctor Bucarey, Sophia Calderón, Gonzalo Muñoz, Frédéric Semet. Decision-focused predictions via pessimistic bilevel optimization: a computational study. 2023. ⟨hal-04397536⟩
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