Decision-focused learning integrates predictive modeling and combinatorial optimization by training models to directly improve decision quality rather than prediction accuracy alone. Differentiating through combinatorial optimization problems represents a central challenge, and recent approaches tackle this difficulty by introducing perturbation-based approximations. In this work, we focus on estimating the objective function coefficients of a combinatorial optimization problem. Our study demonstrates that fluctuations in perturbation intensity occurring during the learning phase can lead to ineffective training, by establishing a theoretical link to the notion of solution stability in combinatorial optimization. We propose addressing this issue by introducing a regularization of the estimated cost vectors which improves the robustness and reliability of the learning process, as demonstrated by extensive numerical experiments.

翻译：决策导向学习通过训练模型直接提升决策质量而非单纯追求预测精度，实现了预测建模与组合优化的深度融合。对组合优化问题进行可微化处理是该领域的核心挑战，近期研究通过引入基于扰动的近似方法来解决这一难题。本文聚焦于组合优化问题目标函数系数的估计研究。通过建立与组合优化中解决方案稳定性概念的理论联系，我们证明了学习阶段扰动强度的波动可能导致训练失效。为此，我们提出对估计成本向量进行正则化处理的方法，大量数值实验表明该方法能有效提升学习过程的鲁棒性与可靠性。