Home > Publications database > MirrorCBO: A consensus-based optimization method in the spirit of mirror descent > print

001     640480
005     20251217132559.0
024 7 _ |a arXiv:2501.12189
|2 arXiv
037 _ _ |a PUBDB-2025-04802
041 _ _ |a English
088 _ _ |a arXiv:2501.12189
|2 arXiv
100 1 _ |a Bungert, Leon
|b 0
245 _ _ |a MirrorCBO: A consensus-based optimization method in the spirit of mirror descent
260 _ _ |c 2025
336 7 _ |a Preprint
|b preprint
|m preprint
|0 PUB:(DE-HGF)25
|s 1762864366_1868919
|2 PUB:(DE-HGF)
336 7 _ |a WORKING_PAPER
|2 ORCID
336 7 _ |a Electronic Article
|0 28
|2 EndNote
336 7 _ |a preprint
|2 DRIVER
336 7 _ |a ARTICLE
|2 BibTeX
336 7 _ |a Output Types/Working Paper
|2 DataCite
500 _ _ |a 66 pages, 18 figures, 19 tables
520 _ _ |a In this work we propose MirrorCBO, a consensus-based optimization (CBO) method which generalizes standard CBO in the same way that mirror descent generalizes gradient descent. For this we apply the CBO methodology to a swarm of dual particles and retain the primal particle positions by applying the inverse of the mirror map, which we parametrize as the subdifferential of a strongly convex function $ϕ$. In this way, we combine the advantages of a derivative-free non-convex optimization algorithm with those of mirror descent. As a special case, the method extends CBO to optimization problems with convex constraints. Assuming bounds on the Bregman distance associated to $ϕ$, we provide asymptotic convergence results for MirrorCBO with explicit exponential rate. Another key contribution is an exploratory numerical study of this new algorithm across different application settings, focusing on (i) sparsity-inducing optimization, and (ii) constrained optimization, demonstrating the competitive performance of MirrorCBO. We observe empirically that the method can also be used for optimization on (non-convex) submanifolds of Euclidean space, can be adapted to mirrored versions of other recent CBO variants, and that it inherits from mirror descent the capability to select desirable minimizers, like sparse ones. We also include an overview of recent CBO approaches for constrained optimization and compare their performance to MirrorCBO.
536 _ _ |a 623 - Data Management and Analysis (POF4-623)
|0 G:(DE-HGF)POF4-623
|c POF4-623
|f POF IV
|x 0
536 _ _ |a DFG project G:(GEPRIS)544579844 - GeoMAR: Geometrische Methoden für Adversarial Robustness (544579844)
|0 G:(GEPRIS)544579844
|c 544579844
|x 1
588 _ _ |a Dataset connected to DataCite
693 _ _ |0 EXP:(DE-MLZ)NOSPEC-20140101
|5 EXP:(DE-MLZ)NOSPEC-20140101
|e No specific instrument
|x 0
700 1 _ |a Hoffmann, Franca
|b 1
700 1 _ |a Kim, Dohyeon
|0 P:(DE-HGF)0
|b 2
|e Corresponding author
700 1 _ |a Roith, Tim
|0 P:(DE-H253)PIP1106486
|b 3
|u desy
856 4 _ |u https://bib-pubdb1.desy.de/record/640480/files/2501.12189v2.pdf
|y Restricted
856 4 _ |u https://bib-pubdb1.desy.de/record/640480/files/2501.12189v2.pdf?subformat=pdfa
|x pdfa
|y Restricted
909 C O |o oai:bib-pubdb1.desy.de:640480
|p VDB
910 1 _ |a Deutsches Elektronen-Synchrotron
|0 I:(DE-588b)2008985-5
|k DESY
|b 3
|6 P:(DE-H253)PIP1106486
910 1 _ |a External Institute
|0 I:(DE-HGF)0
|k Extern
|b 3
|6 P:(DE-H253)PIP1106486
913 1 _ |a DE-HGF
|b Forschungsbereich Materie
|l Materie und Technologie
|1 G:(DE-HGF)POF4-620
|0 G:(DE-HGF)POF4-623
|3 G:(DE-HGF)POF4
|2 G:(DE-HGF)POF4-600
|4 G:(DE-HGF)POF
|v Data Management and Analysis
|x 0
914 1 _ |y 2025
915 _ _ |a Published
|0 StatID:(DE-HGF)0580
|2 StatID
920 1 _ |0 I:(DE-H253)FS-CI-20230420
|k FS-CI
|l Computational Imaging
|x 0
980 _ _ |a preprint
980 _ _ |a VDB
980 _ _ |a I:(DE-H253)FS-CI-20230420
980 _ _ |a UNRESTRICTED

LibraryCollectionCLSMajorCLSMinorLanguageAuthor
Marc 21