Ensemble-Based Gradient Inference for Particle Methods in Optimization and Sampling

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dc.contributor.authorSchillings , Claudia
dc.contributor.authorTotzeck , Claudia
dc.contributor.authorWacker, Philipp
dc.date.accessioned2024-01-21T21:22:02Z
dc.date.available2024-01-21T21:22:02Z
dc.date.issued2023
dc.date.updated2023-07-11T01:25:58Z
dc.description.abstractWe 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 V 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
dc.identifier.citationSchillings C, Totzeck C, Wacker P (2023). Ensemble-Based Gradient Inference for Particle Methods in Optimization and Sampling. Ensemble-Based Gradient Inference for Particle Methods in Optimization and Sampling. 11(3). 757-787.
dc.identifier.doihttp://doi.org/10.1137/22M1533281
dc.identifier.urihttps://hdl.handle.net/10092/106663
dc.rightsAll rights reserved unless otherwise stated
dc.rights.urihttp://hdl.handle.net/10092/17651
dc.subjectoptimization
dc.subjectsampling
dc.subjectLangevin dynamics
dc.subjectensemble methods
dc.subject.anzsrc49 - Mathematical sciences::4903 - Numerical and computational mathematics::490304 - Optimisation
dc.subject.anzsrc49 - Mathematical sciences::4905 - Statistics
dc.titleEnsemble-Based Gradient Inference for Particle Methods in Optimization and Sampling
dc.typeJournal Article
uc.collegeFaculty of Engineering
uc.departmentMathematics and Statistics
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