Learning to Optimize Contextually Constrained Problems for Real-Time Decision Generation

Aaron Babier (), Timothy C. Y. Chan (), Adam Diamant () and Rafid Mahmood ()
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Aaron Babier: Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada
Timothy C. Y. Chan: Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada
Adam Diamant: Schulich School of Business, York University, Toronto, Ontario M3J 1P3, Canada
Rafid Mahmood: Telfer School of Management, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

Management Science, 2025, vol. 71, issue 2, 1165-1186

Abstract: The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities. In this paper, we combine ideas from both fields to address the problem of learning to generate decisions to instances of optimization problems with potentially nonlinear or nonconvex constraints where the feasible set varies with contextual features. We propose a novel framework for training a generative model to produce provably optimal decisions by combining interior point methods and adversarial learning, which we further embed within an iterative data generation algorithm. To this end, we first train a classifier to learn feasibility and then train the generative model to produce optimal decisions to an optimization problem using the classifier as a regularizer. We prove that decisions generated by our model satisfy in-sample and out-of-sample optimality guarantees. Furthermore, the learning models are embedded in an active learning loop in which synthetic instances are iteratively added to the training data; this allows us to progressively generate provably tighter optimal decisions. We investigate case studies in portfolio optimization and personalized treatment design, demonstrating that our approach yields advantages over predict-then-optimize and supervised deep learning techniques, respectively. In particular, our framework is more robust to parameter estimation error compared with the predict-then-optimize paradigm and can better adapt to domain shift as compared with supervised learning models.

Keywords: data-driven decision making; deep learning; portfolio optimization; cancer therapy (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:71:y:2025:i:2:p:1165-1186

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