通过成本正则化提升决策导向学习中的解稳定性。
Managing Solution Stability in Decision-Focused Learning with Cost Regularization
- 引入成本向量正则化，增强优化解的稳定性。
- 实验表明该方法显著提升训练可靠性与决策质量。
- 适合需要稳定优化结果的工业决策场景。
决策导向学习将预测建模与组合优化相结合，通过直接优化决策质量而非仅提升预测准确率来训练模型。区分组合优化问题构成核心挑战，近期方法采用扰动近似解决此难题。本文聚焦于估计组合优化问题的目标函数系数，研究发现训练过程中扰动强度的波动会导致训练失效，其根源在于组合优化中的解稳定性问题。为此，我们提出对估计的成本向量施加正则化，显著提升了学习过程的鲁棒性与可靠性，大量数值实验验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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