Ensemble-based gradient inference for particle methods in optimization
and sampling
- URL: http://arxiv.org/abs/2209.15420v1
- Date: Fri, 23 Sep 2022 09:21:35 GMT
- Title: Ensemble-based gradient inference for particle methods in optimization
and sampling
- Authors: Claudia Schillings and Claudia Totzeck and Philipp Wacker
- Abstract summary: We propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information.
We suggest to use this information for the improvement of established ensemble-based numerical methods for optimization and sampling.
- Score: 2.9005223064604078
- License: http://creativecommons.org/licenses/by-sa/4.0/
- 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).
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