A Survey and Taxonomy of Loss Functions in Machine Learning

Lorenzo Ciampiconi, Adam Elwood, Marco Leonardi, Ashraf Mohamed, Alessandro Rozza

Most state-of-the-art machine learning techniques revolve around the optimization of loss functions, making the choice of an objective critical to model performance and reliability. Although recent reviews discuss loss functions in specific domains or in deep learning settings, there is still no single reference that presents widely used losses across major task families within a unified formal setting and with consistent optimization-relevant property annotations. In this survey, we compile and systematize the most widely adopted loss functions for regression, classification, generative modeling, ranking, energy-based modeling, and relational learning. Our selection procedure combines seeding from foundational textbooks and prior surveys with cross-checking of highly cited literature and common implementations in mainstream machine learning frameworks. We introduce 52 loss functions and organize them into an intuitive taxonomy, summarizing their theoretical motivation, key mathematical properties, and typical application contexts, with compact appendix tables for quick lookup. This survey is intended as a resource for undergraduate, graduate, and Ph.D. students, as well as researchers seeking a structured reference for selecting and comparing loss functions.