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arXiv · 2505.14389

Accelerating Diagonal Methods for Bilevel Optimization: Unified Convergence via Continuous-Time Dynamics

Radu Ioan Boţ·Enis Chenchene·Ernö Robert Csetnek·David Alexander Hulett
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Abstract

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 H\"olderian 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.

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Radu Ioan Boţ, Enis Chenchene, Ernö Robert Csetnek, David Alexander Hulett. 2025-05-20. Accelerating Diagonal Methods for Bilevel Optimization: Unified Convergence via Continuous-Time Dynamics. https://arxiv.org/abs/2505.14389

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