逆线性最优化模型拟合与评价的包围学习框架
An Ensemble Learning Framework for Model Fitting and Evaluation in Inverse Linear Optimization
摘要：
我们开发了一个广义逆优化框架，用于拟合给定多个观测决策的单个线性最优化问题的成本向量。这种设置的动机是集成学习，其中从基本学习者建立共识可以产生更好的预测。我们统一在一个单一的框架下的逆优化文献中的几个模型，并推导出无约束和精确解的方法。我们扩展了一个良好的拟合度量先前介绍的问题与一个单一的观察到的决定，这个新的设置，并证明了几个重要的属性。最后，我们展示了我们的框架，在一个新的逆优化驱动的自动化放射治疗治疗计划的过程。这里，逆最优化模型利用来自不同机器学习模型的剂量预测的集合来构建优于基线方法的共识治疗计划。共识计划在用于计划评价的竞争性临床标准之间产生更好的权衡。
英文摘要：
We develop a generalized inverse optimization framework for fitting the cost vector of a single linear optimization problem given multiple observed decisions. This setting is motivated by ensemble learning, where building consensus from base learners can yield better predictions. We unify several models in the inverse optimization literature under a single framework and derive assumption-free and exact solution methods for each one. We extend a goodness-of-fit metric previously introduced for the problem with a single observed decision to this new setting, and demonstrate several important properties. Finally, we demonstrate our framework in a novel inverse optimization-driven procedure for automated radiation therapy treatment planning. Here, the inverse optimization model leverages an ensemble of dose predictions from different machine learning models to construct a consensus treatment plan that outperforms baseline methods. The consensus plan yields better trade-offs between the competing clinical criteria used for plan evaluation.
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