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.

不确定性优化参数的处理是一个重要且长期存在的挑战，本研究致力于通过构建决策导向的预测模型来减少决策对不确定参数的敏感性，并将其建模为一种非凸二次优化问题以实现可行性。

决策导向的预测：悲观双层优化的计算研究