There is a recent proliferation of research on the integration of machine learning and optimization. One expansive area within this research stream is predictive-model embedded optimization, which proposes the use of pre-trained predictive models as surrogates for uncertain or highly complex objective functions. In this setting, features of the predictive models become decision variables in the optimization problem. Despite a recent surge in publications in this area, only a few papers note the importance of incorporating trust region considerations in this decision-making pipeline, i.e., enforcing solutions to be similar to the data used to train the predictive models. Without such constraints, the evaluation of the predictive model at solutions obtained from optimization cannot be trusted and the practicality of the solutions may be unreasonable. In this paper, we provide an overview of the approaches appearing in the literature to construct a trust region, and propose three alternative approaches. Our numerical evaluation highlights that trust-region constraints learned through isolation forests, one of the newly proposed approaches, outperform all previously suggested approaches, both in terms of solution quality and computational time.
翻译:最近,关于集成机器学习和优化的研究大量增加。这一研究流中一个广泛的领域是预测模型嵌入优化,其中提议使用预先训练的预测模型来替代不确定或高度复杂的客观功能。在这种背景下,预测模型的特点成为优化问题的决策变量。尽管最近这一领域的出版物激增,但只有几份文件指出,必须将信任区域考虑纳入这一决策管道,即强制采用类似于用于培训预测模型的数据的解决办法。没有这些限制,对从优化中获得的解决方案的预测模型的评价就无法令人信服,解决方案的实用性可能不合理。在本文件中,我们概述了文献中出现的建立信任区域的方法,并提出了三种备选方法。我们的数字评价强调,通过孤立森林学习的信任区域制约是新提出的办法之一,在解决方案质量和计算时间方面都不符合所有先前建议的办法。