Repository: Freie Universit├Ąt Berlin, Math Department

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

Schillings, Claudia and Totzeck, Claudia and Wacker, Philipp (2023) Ensemble-based gradient inference for particle methods in optimization and sampling. SIAM/ASA Journal on Uncertainty Quantification, 11 (3). pp. 757-787.

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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 of some potential in an ensemble 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 ( Claudia , Claudia , Philipp

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group
ID Code:2982
Deposited By: Ulrike Eickers
Deposited On:22 May 2023 12:34
Last Modified:20 Feb 2024 06:35

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