arXiv Statistics ML

Outperformance Inverse Optimization: Learning Objective Functions that Outperform Agent Decisions

arXiv AI
Sep 10

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

The paper presents a unified taxonomy that classifies machine‑learning and artificial‑intelligence applications according to mathematical programming paradigms such as linear, quadratic, mixed‑integer, conic, bilevel, and others. It standardizes notation, identifies key inputs, decision variables, and principal formulations for each application, and discusses structural properties, solution strategies, and limitations. The authors compare tractability, relaxation quality, decomposition, approximation guarantees, and scalability across paradigms, emphasizing that mathematical programming serves as a disciplined interface between predictions and constrained decisions rather than a universal modeling claim.

By Chaosheng Dong
arXiv Machine Learning
Aug 20

Escaping Local Minima Provably in Non-convex Matrix Sensing: A Deterministic Framework via Simulated Lifting

The paper introduces a deterministic Simulated Oracle Direction (SOD) framework that enables escaping spurious local minima in non‑convex low‑rank matrix sensing without explicit tensor lifting. By projecting over‑parameterized escape directions back into the original parameter space, the method guarantees a strict decrease in objective value from existing local minima. Experiments show reliable escape from local minima and convergence to global optima with minimal computational overhead compared to explicit over‑parameterization.

By Tianqi Shen, Jinji Yang, Junze He, Kunhan Gao, Zeyu Zheng, Ziye Ma