Mathematical programming unifies many machine learning decisions
Mathematical Programming in Machine Learning and Artificial Intelligence: A Unified Taxonomy of Models and Applications
Artificial Intelligence
Summary
Many decisions in AI and machine learning, like how to route data or balance goals, can be described using mathematical programs. The authors organize different models and applications in one common framework, showing how they compare and work. This helps clarify how math helps make decisions in AI systems, without oversimplifying them to just a few types of problems.
What this means in practice
- •For machine learning engineers: Design constrained prediction models using a unified optimization framework to handle multiple objectives and distribution shifts.
- •For natural language processing teams: Optimize token routing and retrieval context selection within NLP pipelines using structured mathematical programs.
A survey. It maps existing work.
Authors
Chaosheng Dong
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.