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Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization

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dc.affiliation.dptoUC3M. Departamento de Teoría de la Señal y Comunicacioneses
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Tratamiento de la Señal y Aprendizaje (GTSA)es
dc.contributor.authorAkyildiz, Omer Deniz
dc.contributor.authorCrisan, Dan
dc.contributor.authorMíguez Arenas, Joaquín
dc.contributor.funderComunidad de Madrides
dc.contributor.funderAgencia Estatal de Investigación (España)es
dc.date.accessioned2023-07-14T07:24:35Z
dc.date.available2023-07-14T07:24:35Z
dc.date.issued2020-11
dc.description.abstractWe introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth-order optimization algorithm which demands only the capability to evaluate small subsets of components of the cost function. It can be depicted as a bank of samplers that generate particle approximations of several sequences of probability measures. These measures are constructed in such a way that they have associated probability density functions whose global maxima coincide with the global minima of the original cost function. The algorithm selects the best performing sampler and uses it to approximate a global minimum of the cost function. We prove analytically that the resulting estimator converges to a global minimum of the cost function almost surely and provide explicit convergence rates in terms of the number of generated Monte Carlo samples and the dimension of the search space. We show, by way of numerical examples, that the algorithm can tackle cost functions with multiple minima or with broad "flat" regions which are hard to minimize using gradient-based techniques.en
dc.description.sponsorshipThis work was partially supported by Agencia Estatal de Investigación of Spain (RTI2018-099655-B-I00 CLARA), and the regional government of Madrid (program CASICAM-CM S2013/ICE-2845). The work of the second author has been partially supported by a UC3M-Santander Chair of Excellence grant held at the Universidad Carlos III de Madrid.en
dc.format.extent19
dc.identifier.bibliographicCitationAkyildiz, Ö. D., Crisan, D., & Míguez, J. (2020). Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization. Statistics and Computing, 30(6), 1645-1663.en
dc.identifier.doihttps://doi.org/10.1007/s11222-020-09964-4
dc.identifier.issn0960-3174
dc.identifier.publicationfirstpage1645
dc.identifier.publicationissue6
dc.identifier.publicationlastpage1663
dc.identifier.publicationtitleStatistics and Computingen
dc.identifier.publicationvolume30
dc.identifier.urihttps://hdl.handle.net/10016/37838
dc.identifier.uxxiAR/0000027719
dc.language.isoeng
dc.publisherSpringeren
dc.relation.projectIDComunidad de Madrid. S2013/ICE-2845es
dc.relation.projectIDGobierno de España. RTI2018-099655-B-I00es
dc.rights© The Author(s) 2020.en
dc.rightsAtribución 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/*
dc.subject.ecienciaBiología y Biomedicinaes
dc.subject.ecienciaCiencias de la Informaciónes
dc.subject.ecienciaEconomíaes
dc.subject.ecienciaElectrónicaes
dc.subject.ecienciaEstadísticaes
dc.subject.ecienciaTelecomunicacioneses
dc.subject.otherSequential Monte Carloen
dc.subject.otherStochastic optimizationen
dc.subject.otherNonconvex optimizationen
dc.subject.otherGradient-free optimizationen
dc.subject.otherSamplingen
dc.titleParallel sequential Monte Carlo for stochastic gradient-free nonconvex optimizationen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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