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

arXiv: https://arxiv.org/abs/2505.14389 · HTML: https://mlsanity.com/paper/2505.14389/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2025.

## Built on by (most cited first, 1 of 1)

- [Stochastic variance reduced extragradient methods for solving hierarchical variational inequalities](https://mlsanity.com/paper/2602.13510/) (2026)

## Abstract (arXiv)

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.