Accelerating Diagonal Methods for Bilevel Optimization: Unified Convergence via Continuous-Time Dynamics
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908372302823424 |
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| author | Boţ, Radu Ioan Chenchene, Enis Csetnek, Ernö Robert Hulett, David Alexander |
| author_facet | Boţ, Radu Ioan Chenchene, Enis Csetnek, Ernö Robert Hulett, David Alexander |
| contents | We analyze fast diagonal methods for simple bilevel programs. Guided by the analysis of the corresponding continuous-time dynamics, we provide a unified convergence analysis under general geometric conditions, including Hölderian growth and the Attouch-Czarnecki condition. Our results yield explicit convergence rates and guarantee weak convergence to a solution of the bilevel problem. In particular, we improve and extend recent results on accelerated schemes, offering novel insights into the trade-offs between geometry, regularization decay, and algorithmic design. Numerical experiments illustrate the advantages of more flexible methods and support our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14389 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accelerating Diagonal Methods for Bilevel Optimization: Unified Convergence via Continuous-Time Dynamics Boţ, Radu Ioan Chenchene, Enis Csetnek, Ernö Robert Hulett, David Alexander Optimization and Control 90C25, 91A65, 90C99, 37L05, 65K10, 65K05, 46N10 We analyze fast diagonal methods for simple bilevel programs. Guided by the analysis of the corresponding continuous-time dynamics, we provide a unified convergence analysis under general geometric conditions, including Hölderian growth and the Attouch-Czarnecki condition. Our results yield explicit convergence rates and guarantee weak convergence to a solution of the bilevel problem. In particular, we improve and extend recent results on accelerated schemes, offering novel insights into the trade-offs between geometry, regularization decay, and algorithmic design. Numerical experiments illustrate the advantages of more flexible methods and support our theoretical findings. |
| title | Accelerating Diagonal Methods for Bilevel Optimization: Unified Convergence via Continuous-Time Dynamics |
| topic | Optimization and Control 90C25, 91A65, 90C99, 37L05, 65K10, 65K05, 46N10 |
| url | https://arxiv.org/abs/2505.14389 |