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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Boţ, Radu Ioan, Chenchene, Enis, Csetnek, Ernö Robert, Hulett, David Alexander
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908372302823424
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