Research
Mathematical Programming in Machine Learning and Artificial Intelligence: A Unified Taxonomy of Models and Applications
arXiv:2609.07254v1 Announce Type: cross Abstract: Mathematical programming provides a common language for many decisions embedded in modern machine-learning (ML) and artificial-intelligence (AI) syste
arXiv:2609.07254v1 Announce Type: cross 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.
Related
- Wolkowicz-Styan Upper Bound on the Hessian Eigenspectrum for Cross-Entropy Loss in Nonlinear Smooth Neural Networks
- MiMuon: Mixed Muon Optimizer with Improved Generalization for Large Models
- The Role of Gradient Modification in Heavy-Tailed Nonconvex Stochastic Min-Max Optimization
Source: arXiv cs.AI | 2026-09-10