分位数逆Optimization：提高逆线性规划的稳定性
Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming
摘要：
逆线性规划（LP）由于其生成高效优化公式的潜力而受到越来越多的关注，所述优化公式可以紧密地复制复杂系统的行为。然而，从现有的逆LP方法逆推断的参数和相应的正解可能对输入数据中的噪声、误差和不确定性高度敏感，限制了其在数据驱动设置中的适用性。我们介绍了逆LP的逆和前向稳定性的概念，并提出了一种新的逆LP方法，确定了一组目标函数是稳定的数据不完善和产生的解决方案接近的相关子集的数据。我们制定的逆模型作为一个混合整数规划，并阐明其连接到双团问题，我们利用开发有效的prostitics。我们还展示了如何将这种方法用于在线学习。我们数值评估所提出的方法的稳定性，并证明其在饮食建议和转运应用程序的实际用途。
英文摘要：
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and corresponding forward solutions from the existing inverse LP method can be highly sensitive to noise, errors, and uncertainty in the input data, limiting its applicability in data-driven settings. We introduce the notion of inverse and forward stability in inverse LP and propose a novel inverse LP method that determines a set of objective functions that are stable under data imperfection and generate solutions close to the relevant subset of the data. We formulate the inverse model as a mixed-integer program and elucidate its connection to bi-clique problems, which we exploit to develop efficient heuristics. We also show how this method can be used for online learning. We numerically evaluate the stability of the proposed method and demonstrate its practical use in the diet recommendation and transshipment applications.
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