CBX: Python and Julia Packages for Consensus-Based
Interacting Particle Methods

Bailo, Rafael; Barbaro, Alethea; Gomes, Susana N.; Riedl, Konstantin; Roith, Tim; Totzeck, Claudia; Vaes, Urbain

doi:10.21105/joss.06611

JOSS

2024

DOI: 10.21105/joss.06611

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CBX: Python and Julia Packages for Consensus-Based Interacting Particle Methods

Rafael Bailo,

Alethea Barbaro,

Susana N. Gomes

et al.

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2024

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Polarized consensus-based dynamics for optimization and sampling

Bungert,

Roith,

Wacker

2024

Math. Program.

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In this paper we propose polarized consensus-based dynamics in order to make consensus-based optimization (CBO) and sampling (CBS) applicable for objective functions with several global minima or distributions with many modes, respectively. For this, we “polarize” the dynamics with a localizing kernel and the resulting model can be viewed as a bounded confidence model for opinion formation in the presence of common objective. Instead of being attracted to a common weighted mean as in the original consensus-based methods, which prevents the detection of more than one minimum or mode, in our method every particle is attracted to a weighted mean which gives more weight to nearby particles. We prove that in the mean-field regime the polarized CBS dynamics are unbiased for Gaussian targets. We also prove that in the zero temperature limit and for sufficiently well-behaved strongly convex objectives the solution of the Fokker–Planck equation converges in the Wasserstein-2 distance to a Dirac measure at the minimizer. Finally, we propose a computationally more efficient generalization which works with a predefined number of clusters and improves upon our polarized baseline method for high-dimensional optimization.

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Polarized consensus-based dynamics for optimization and sampling

Bungert,

Roith,

Wacker

2024

Math. Program.

View full text Add to dashboard Cite

show abstract

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CBX: Python and Julia Packages for Consensus-Based Interacting Particle Methods

Cited by 1 publication

References 48 publications

Polarized consensus-based dynamics for optimization and sampling

Polarized consensus-based dynamics for optimization and sampling

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