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There is a recent proliferation of research on the integration of machinelearning and optimization. One expansive area within this research stream ispredictive-model embedded optimization, which proposes the use of pre-trainedpredictive models as surrogates for uncertain or highly complex objectivefunctions. In this setting, features of the predictive models become decisionvariables in the optimization problem. Despite a recent surge in publicationsin this area, only a few papers note the importance of incorporating trustregion considerations in this decision-making pipeline, i.e., enforcingsolutions to be similar to the data used to train the predictive models.Without such constraints, the evaluation of the predictive model at solutionsobtained from optimization cannot be trusted and the practicality of thesolutions may be unreasonable. In this paper, we provide an overview of theapproaches appearing in the literature to construct a trust region, and proposethree alternative approaches. Our numerical evaluation highlights thattrust-region constraints learned through isolation forests, one of the newlyproposed approaches, outperform all previously suggested approaches, both interms of solution quality and computational time.

Constraint Learning to Define Trust Regions in Predictive-Model Embedded Optimization