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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2604.05678 |
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| _version_ | 1866913010146082816 |
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| author | Bounja, Karim Achchab, Boujemaâ Sakat, Abdeljalil |
| author_facet | Bounja, Karim Achchab, Boujemaâ Sakat, Abdeljalil |
| contents | We introduce a natural displacement control for minimizer sets of oracle objectives equipped with certified epigraphic information. Formally, we replace the usual local uniform value control of objective perturbations - uncertifiable from finite pointwise information without additional structure - by the strictly weaker requirement of a cylinder-localized vertical epigraphic control, naturally provided by certified envelopes. Under set-based quadratic growth (allowing nonunique minimizers), this yields the classical square-root displacement estimate with optimal exponent 1/2, without any extrinsic assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05678 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Intrinsic perturbation scale for certified oracle objectives with epigraphic information Bounja, Karim Achchab, Boujemaâ Sakat, Abdeljalil Optimization and Control Machine Learning Functional Analysis 49J52, 90C31, 49J53, 49J45 We introduce a natural displacement control for minimizer sets of oracle objectives equipped with certified epigraphic information. Formally, we replace the usual local uniform value control of objective perturbations - uncertifiable from finite pointwise information without additional structure - by the strictly weaker requirement of a cylinder-localized vertical epigraphic control, naturally provided by certified envelopes. Under set-based quadratic growth (allowing nonunique minimizers), this yields the classical square-root displacement estimate with optimal exponent 1/2, without any extrinsic assumption. |
| title | Intrinsic perturbation scale for certified oracle objectives with epigraphic information |
| topic | Optimization and Control Machine Learning Functional Analysis 49J52, 90C31, 49J53, 49J45 |
| url | https://arxiv.org/abs/2604.05678 |