Mathematical Programming in Machine Learning and Artificial Intelligence: A Unified Taxonomy of Models and Applications

• URL: http://arxiv.org/abs/2609.07254v1
• Date: Mon, 07 Sep 2026 09:10:54 GMT
• Title: Mathematical Programming in Machine Learning and Artificial Intelligence: A Unified Taxonomy of Models and Applications
• Abstract summary: This paper organizes various applications under common mathematical programming paradigms.<n>We normalize the models with a mostly unified notation and, for every application, identify inputs, decision variables, a principal formulation, structural properties, solution strategies, and limitations.<n>The paper shows that mathematical programming is most useful not as a claim that all learning is LP or MIP, but as a disciplined interface between predictions and constrained decisions.
• Score: 11.680598532247737
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Mathematical programming provides a common language for many decisions embedded in modern machine-learning (ML) and artificial-intelligence (AI) systems: selecting retrieval context, routing tokens, allocating inference compute, fitting structured predictors, protecting against distribution shift, and balancing competing objectives. However, the relevant literature is fragmented across optimization, information retrieval, recommendation, natural-language processing, computer vision, and learning theory. This paper organizes various applications under common mathematical programming paradigms: linear, quadratic, binary and mixed-integer, conic, bilevel, multi-objective, inverse, distributionally robust, submodular, and min--max optimization. We normalize the models with a mostly unified notation and, for every application, identify inputs, decision variables, a principal formulation, structural properties, solution strategies, and limitations. Across paradigms, we compare tractability, relaxation quality, decomposition, approximation guarantees, and scalability bottlenecks. The paper shows that mathematical programming is most useful not as a claim that all learning is LP or MIP, but as a disciplined interface between predictions and constrained decisions.

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