🤖 AI Summary
To address the high sensitivity of decisions to parameter uncertainty arising from the decoupled prediction–optimization paradigm, this paper proposes a decision-focused prediction framework that minimizes expected regret. Methodologically, it formulates expected regret minimization as a pessimistic bilevel optimization problem—the first such formulation—and proves its NP-hardness. Leveraging Lagrangian duality theory, the problem is equivalently reformulated as a solvable nonconvex quadratic program. To ensure computational tractability, the approach integrates heuristic computation with exact algorithms for efficient solving. Empirically evaluated on shortest-path problems with uncertain edge weights, the method substantially outperforms the state-of-the-art approach by Elmachtoub & Grigas (2022), achieving significant improvements in both training efficiency and decision robustness under uncertainty.
📝 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.
