Accelerating diagonal methods for bilevel optimization: Unified convergence via continuous-time dynamics

• 成果类型: Article; Early Access
• 署名作者: Bot, Radu I.; Chenchene, Enis; Csetnek, E. Robert; Hulett, David A.
• 署名单位: University of Vienna
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-026-02376-8
• 发表日期: 2026-07-08
• 关键词: bilevel optimization; tikhonov regularization; Nesterov momentum; convergence rates; Lyapunov analysis; diagonal scheme; VISCOSITY SOLUTIONS; convex; algorithm

摘要

We analyze fast diagonal methods for simple bilevel programs. Guided by the analysis of the corresponding continuous-time dynamics, under a mild general assumption we provide convergence rates for the inner residual and upper bounds for the outer residual along an ergodic sequence. As the key point of our work, under geometric assumptions for the inner function-namely, a weaker condition attributed to Attouch and Czarnecki and a stronger H & ouml;lderian error bound-we provide a unified convergence analysis, which yields explicit last-iterate convergence rates and guarantees 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.