{"ID":2886273,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.03314","arxiv_id":"2508.03314","title":"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.","short_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...","url_abs":"https://arxiv.org/abs/2508.03314","url_pdf":"https://arxiv.org/pdf/2508.03314v1","authors":"[\"Francisco Daunas\",\"Iñaki Esnaola\",\"Samir M. Perlaza\"]","published":"2025-08-05T10:48:40Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}