# Generalization Error of f-Divergence Stabilized Algorithms via Duality

arXiv: https://arxiv.org/abs/2502.14544 · HTML: https://mlsanity.com/paper/2502.14544/

## Key facts

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- First posted on arXiv 20 Feb 2025.

## Abstract (arXiv)

The solution to empirical risk minimization with f-divergence regularization (ERM-fDR) is extended to constrained optimization problems, establishing conditions for equivalence between the solution and constraints. A dual formulation of ERM-fDR is introduced, providing a computationally efficient method to derive the normalization function of the ERM-fDR 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-fDR solutions.