Constraint Learning to Define Trust Regions in Optimization over Pre-Trained Predictive Models

Chenbo Shi (), Mohsen Emadikhiav (), Leonardo Lozano () and David Bergman ()
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Chenbo Shi: Department of Operations and Information Management, University of Connecticut, Storrs, Connecticut 06268
Mohsen Emadikhiav: Department of Information Technology and Operations Management, Florida Atlantic University, Boca Raton, Florida 33431
Leonardo Lozano: Department of Operations, Business Analytics, and Information Systems, University of Cincinnati, Cincinnati, Ohio 45221
David Bergman: Department of Operations and Information Management, University of Connecticut, Storrs, Connecticut 06268

INFORMS Journal on Computing, 2024, vol. 36, issue 6, 1382-1399

Abstract: There is a recent proliferation of research on the integration of machine learning and optimization. One expansive area within this research stream is optimization over pre-trained predictive models, 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, that is, 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 our newly proposed approaches compare favorably with previously suggested approaches, both in terms of solution quality and computational time.

Keywords: data-driven decision making; integration of machine learning and optimization; trust region; constraint learning; isolation forest (search for similar items in EconPapers)
Date: 2024
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