Global Optimization Algorithm through High-Resolution Sampling

TL;DR

This paper introduces a novel global optimization algorithm leveraging high-resolution sampling inspired by Langevin dynamics, capable of efficiently finding the global minimum of nonconvex functions under certain probabilistic conditions.

Contribution

It proposes a new sampling-based optimization method and a high-resolution sampling algorithm inspired by Langevin dynamics, advancing theoretical understanding and practical performance.

Findings

Outperforms recent approaches on the Rastrigin function

Provides theoretical guarantees under logarithmic Sobolev inequality

Introduces a high-resolution sampling algorithm for global optimization

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.