Global Optimization Algorithm through High-Resolution Sampling
Abstract
We present an optimization algorithm that can identify a global minimum of a potentially nonconvex smooth function with high probability, assuming the Gibbs measure of the potential satisfies a logarithmic Sobolev inequality. Our contribution is twofold: on the one hand we propose a global optimization method, which is built on an oracle sampling algorithm producing arbitrarily accurate samples from a given Gibbs measure. On the other hand, we propose a new sampling algorithm, drawing inspiration from both overdamped and underdamped Langevin dynamics, as well as from the high-resolution differential equation known for its acceleration in deterministic settings. While the focus of the paper is primarily theoretical, we demonstrate the effectiveness of our algorithms on the Rastrigin function, where it outperforms recent approaches.
Cite
@article{arxiv.2410.13737,
title = {Global Optimization Algorithm through High-Resolution Sampling},
author = {Daniel Cortild and Claire Delplancke and Nadia Oudjane and Juan Peypouquet},
journal= {arXiv preprint arXiv:2410.13737},
year = {2025}
}