A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913975935959040 |
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| 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 |