A survey and taxonomy of loss functions in machine learning

TL;DR

This survey provides a comprehensive overview and taxonomy of 43 loss functions used across various machine learning tasks, clarifying their properties and optimal applications for researchers and students.

Contribution

It introduces a structured taxonomy of loss functions, offering detailed insights into their theoretical foundations and practical use cases, which was lacking in prior literature.

Findings

Provides a taxonomy of 43 loss functions

Clarifies theoretical foundations and properties

Guides optimal application choices for different tasks

Abstract

Most state-of-the-art machine learning techniques revolve around the optimisation of loss functions. Defining appropriate loss functions is therefore critical to successfully solving problems in this field. In this survey, we present a comprehensive overview of the most widely used loss functions across key applications, including regression, classification, generative modeling, ranking, and energy-based modeling. We introduce 43 distinct loss functions, structured within an intuitive taxonomy that clarifies their theoretical foundations, properties, and optimal application contexts. This survey is intended as a resource for undergraduate, graduate, and Ph.D. students, as well as researchers seeking a deeper understanding of loss functions.