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Generalization Error of $f$-Divergence Stabilized Algorithms via Duality
Francisco Daunas, Iñaki Esnaola, Samir M. Perlaza, Gholamali Ami · 2025-02-20 · via cs.LG updates on arXiv.org

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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