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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.17646 |
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| _version_ | 1866910000047194112 |
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| author | Bounja, Karim Laayouni, Lahcen Sakat, Abdeljalil |
| author_facet | Bounja, Karim Laayouni, Lahcen Sakat, Abdeljalil |
| contents | Empirical risk minimization (ERM) stability is usually studied via single-valued outputs, while convex non-strict losses yield set-valued minimizers. We identify Painlevé-Kuratowski upper semicontinuity (PK-u.s.c.) as the intrinsic stability notion for the ERM solution correspondence (set-level Hadamard well-posedness) and a prerequisite to interpret stability of selections. We then characterize a minimal non-degenerate qualitative regime: Mosco-consistent perturbations and locally bounded minimizers imply PK-u.s.c., minimal-value continuity, and consistency of vanishing-gap near-minimizers. Quadratic growth yields explicit quantitative deviation bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17646 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Mosco sufficient condition for intrinsic stability of non-unique convex Empirical Risk Minimization Bounja, Karim Laayouni, Lahcen Sakat, Abdeljalil Machine Learning Functional Analysis Optimization and Control Statistics Theory Primary: 90C25. Secondary: 49J53, 90C31, 68T05 Empirical risk minimization (ERM) stability is usually studied via single-valued outputs, while convex non-strict losses yield set-valued minimizers. We identify Painlevé-Kuratowski upper semicontinuity (PK-u.s.c.) as the intrinsic stability notion for the ERM solution correspondence (set-level Hadamard well-posedness) and a prerequisite to interpret stability of selections. We then characterize a minimal non-degenerate qualitative regime: Mosco-consistent perturbations and locally bounded minimizers imply PK-u.s.c., minimal-value continuity, and consistency of vanishing-gap near-minimizers. Quadratic growth yields explicit quantitative deviation bounds. |
| title | A Mosco sufficient condition for intrinsic stability of non-unique convex Empirical Risk Minimization |
| topic | Machine Learning Functional Analysis Optimization and Control Statistics Theory Primary: 90C25. Secondary: 49J53, 90C31, 68T05 |
| url | https://arxiv.org/abs/2601.17646 |