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# Learning Classifiers with Fenchel-Young Losses: Generalized Entropies, Margins, and Algorithms

*Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics*, PMLR 89:606-615, 2019.

#### Abstract

This paper studies Fenchel-Young losses, a generic way to construct convex loss functions from a regularization function. We analyze their properties in depth, showing that they unify many well-known loss functions and allow to create useful new ones easily. Fenchel-Young losses constructed from a generalized entropy, including the Shannon and Tsallis entropies, induce predictive probability distributions. We formulate conditions for a generalized entropy to yield losses with a separation margin, and probability distributions with sparse support. Finally, we derive efficient algorithms, making Fenchel-Young losses appealing both in theory and practice.