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.

翻译：处理优化参数中的不确定性是一个重要且长期的挑战。通常，不确定性参数被精确预测，随后求解确定性优化问题。然而，这种所谓"先预测后优化"方法产生的决策可能对不确定性参数高度敏感。本文致力于近期"决策导向"预测的研究，即构建预测模型的目标是最小化基于这些模型所做决策的"遗憾"度量。我们将精确期望遗憾最小化建模为一个悲观双层优化模型。随后，利用对偶论证，将其重新表述为一个非凸二次优化问题。最后，我们展示了多种实现可解性的计算技术。我们针对具有不确定成本向量的最短路径实例进行了广泛的计算实验。结果表明，我们的方法相较于Elmachtoub与Grigas（2022）的先进决策导向学习方法，能够提升训练性能。