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arXiv · 2502.14544

Generalization Error of $f$-Divergence Stabilized Algorithms via Duality

Francisco Daunas·Iñaki Esnaola·Samir M. Perlaza·Gholamali Aminian
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Abstract

The solution to empirical risk minimization with $f$-divergence regularization (ERM-$f$DR) is extended to constrained optimization problems, establishing conditions for equivalence between the solution and constraints. A dual formulation of ERM-$f$DR is introduced, providing a computationally efficient method to derive the normalization function of the ERM-$f$DR solution. This dual approach leverages the Legendre-Fenchel transform and the implicit function theorem, enabling explicit characterizations of the generalization error for general algorithms under mild conditions, and another for ERM-$f$DR solutions.

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Francisco Daunas, Iñaki Esnaola, Samir M. Perlaza, Gholamali Aminian. 2025-02-20. Generalization Error of $f$-Divergence Stabilized Algorithms via Duality. https://arxiv.org/abs/2502.14544

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