Journal Article

PUBDB-2024-01832

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Polarized consensus-based dynamics for optimization and sampling

Bungert, L. ; Roith, T. (Corresponding author)Extern*DESY* ; Wacker, P.

2024
Springer Heidelberg

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Please use a persistent id in citations: doi:10.1007/s10107-024-02095-y  doi:10.3204/PUBDB-2024-01832

Abstract: 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.

Note: L:MB

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Contributing Institute(s):

1. Computational Imaging (FS-CI)

Research Program(s):

1. 623 - Data Management and Analysis (POF4-623) (POF4-623)
2. DFG project G:(GEPRIS)390685689 - EXC 2046: MATH+: Berlin Mathematics Research Center (390685689) (390685689)
3. 05M20WEA - Verbundprojekt 05M2020 - DELETO: Maschinelles Lernen bei korrelativer MR und Hochdurchsatz-NanoCT. Teilvorhaben 3: Gelernte Regularisierungsmethoden und lernbasierte Verfahren für korrelatives MR. (BMBF-05M20WEA) (BMBF-05M20WEA)
4. NoMADS - Nonlocal Methods for Arbitrary Data Sources (777826) (777826)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2024

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; DEAL Springer ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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