A survey and taxonomy of loss functions in machine learning

TL;DR

This survey presents a comprehensive overview of the most widely used loss functions across key applications, including regression, classification, generative modeling, ranking, and energy-based modeling.

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.

Figures (6)

• Figure 1: The proposed taxonomy. Five major tasks are identified on which loss functions are applied, namely regression, classification, ranking, generative and energy-based modeling. Finally, the underlying strategy to optimize them, namely margin-based, probabilistic, and error-based, is illustrated under each group of losses.
• Figure 2: Schematic overview of the regression losses showing the connection
• Figure 3: Overview of the classification losses divided into two major groups: margin-based losses and probabilistic ones.
• Figure 4: Overview of the generative losses.
• Figure 5: Overview of the ranking losses.