Specifying and Solving Robust Empirical Risk Minimization Problems Using CVXPY
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910602813767680 |
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| author | Luxenberg, Eric Malik, Dhruv Li, Yuanzhi Singh, Aarti Boyd, Stephen |
| author_facet | Luxenberg, Eric Malik, Dhruv Li, Yuanzhi Singh, Aarti Boyd, Stephen |
| contents | We consider robust empirical risk minimization (ERM), where model parameters are chosen to minimize the worst-case empirical loss when each data point varies over a given convex uncertainty set. In some simple cases, such problems can be expressed in an analytical form. In general the problem can be made tractable via dualization, which turns a min-max problem into a min-min problem. Dualization requires expertise and is tedious and error-prone. We demonstrate how CVXPY can be used to automate this dualization procedure in a user-friendly manner. Our framework allows practitioners to specify and solve robust ERM problems with a general class of convex losses, capturing many standard regression and classification problems. Users can easily specify any complex uncertainty set that is representable via disciplined convex programming (DCP) constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05649 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Specifying and Solving Robust Empirical Risk Minimization Problems Using CVXPY Luxenberg, Eric Malik, Dhruv Li, Yuanzhi Singh, Aarti Boyd, Stephen Optimization and Control Machine Learning We consider robust empirical risk minimization (ERM), where model parameters are chosen to minimize the worst-case empirical loss when each data point varies over a given convex uncertainty set. In some simple cases, such problems can be expressed in an analytical form. In general the problem can be made tractable via dualization, which turns a min-max problem into a min-min problem. Dualization requires expertise and is tedious and error-prone. We demonstrate how CVXPY can be used to automate this dualization procedure in a user-friendly manner. Our framework allows practitioners to specify and solve robust ERM problems with a general class of convex losses, capturing many standard regression and classification problems. Users can easily specify any complex uncertainty set that is representable via disciplined convex programming (DCP) constraints. |
| title | Specifying and Solving Robust Empirical Risk Minimization Problems Using CVXPY |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2306.05649 |