A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913975935959040 |
|---|---|
| author | Daunas, Francisco Esnaola, Iñaki Perlaza, Samir M. |
| author_facet | Daunas, Francisco Esnaola, Iñaki Perlaza, Samir M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization Daunas, Francisco Esnaola, Iñaki Perlaza, Samir M. Machine Learning 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. |
| title | A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2508.03314 |