A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization
Abstract
The dual formulation of empirical risk minimization with f-divergence regularization (ERM-fDR) is introduced. The solution of the dual optimization problem to the ERM-fDR is connected to the notion of normalization function introduced as an implicit function. This dual approach leverages the Legendre-Fenchel transform and the implicit function theorem to provide a nonlinear ODE expression to the normalization function. Furthermore, the nonlinear ODE expression and its properties provide a computationally efficient method to calculate the normalization function of the ERM-fDR solution under a mild condition.
Cite
@article{arxiv.2508.03314,
title = {A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization},
author = {Francisco Daunas and Iñaki Esnaola and Samir M. Perlaza},
journal= {arXiv preprint arXiv:2508.03314},
year = {2025}
}
Comments
Conference paper to appear in ITW 2025. arXiv admin note: substantial text overlap with arXiv:2502.14544; text overlap with arXiv:2402.00501