Ensemble-based gradient inference for particle methods in optimization and sampling

TL;DR

This paper introduces ensemble-based gradient inference (EGI), a method that extracts derivative information from particle ensembles to enhance optimization and sampling algorithms, improving their ability to explore complex landscapes.

Contribution

The paper presents a novel ensemble-based gradient inference technique that leverages function evaluations to improve existing optimization and sampling methods.

Findings

Augmented algorithms outperform gradient-free variants.

EGI helps escape initial domains and explore multimodal distributions.

Speeds up convergence in optimization dynamics.

Abstract

We propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information of objective functions {from a given ensemble of particles}. Pointwise evaluation $\{V(x^i)\}_i$ of some potential $V$ in an ensemble $\{x^i\}_i$ contains implicit information about first or higher order derivatives, which can be made explicit with little computational effort (ensemble-based gradient inference -- EGI). We suggest to use this information for the improvement of established ensemble-based numerical methods for optimization and sampling such as Consensus-based optimization and Langevin-based samplers. Numerical studies indicate that the augmented algorithms are often superior to their gradient-free variants, in particular the augmented methods help the ensembles to escape their initial domain, to explore multimodal, non-Gaussian settings and to speed up the collapse at the end of optimization dynamics.} The code for the numerical examples in this manuscript can be found in the paper's Github repository (https://github.com/MercuryBench/ensemble-based-gradient.git).