Convergence of Consensus-Based Particle Methods for Nonconvex Bi-Level Optimization
In this paper, we study a consensus-based optimization method for nonconvex bi-level optimization, where the objective is to minimize an upper-level function over the set of global minimizers of a lower-level problem. The proposed approach is derivative-free, and constructs its consensus point via smooth quantile selection combined with a Gibbs-type Laplace approximation. We establish convergence guarantees for both the associated \textit{mean-field} dynamics and its \textit{finite-particle} approximation. In particular, under suitable assumptions on smooth quantile localization, error bounds, and stability, we show that the mean-field law reaches any arbitrary prescribed Wasserstein neig...
| Authors | Yutong Chao, Xudong Sun, Konstantin Riedl et al. |
|---|---|
| Primary category | math.OC |
| Published | 19 May 2026 |
| Last updated at source | 19 May 2026 |
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