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TZID:Europe/Vienna
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DTSTART:20200329T030000
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DTSTART:20191027T020000
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DTSTAMP:20200807T122510Z
UID:5e186a2606102555688253@ist.ac.at
DTSTART:20200124T100000
DTEND:20200124T113000
DESCRIPTION:Speaker: Massimo Fornasier\nhosted by Jan Maas\nAbstract: We in
troduce a new stochastic Kuramoto-Vicsek type model for global optimizatio
n of nonconvex functions on the sphere. This model belongs to the class of
Consensus-Based Optimization methods. In fact\, particles move on the sph
ere driven by a drift towards an instantaneous consensus point\, computed
as a convex combination of the particle locations weighted by the cost fun
ction according to Laplace's principle\, which represents an approximation
to a global minimizer. The dynamics is further perturbed by a random vect
or field to favor exploration\, whose variance is function of the distance
of the particles with respect to the consensus point. In particular\, as
soon as consensus is reached the stochastic component vanishes.In the firs
t part of the talk\, we study the well-posedness of the model and we deriv
e rigorously its mean-field approximation for large particle limit. The ma
in results of the second part of the talk are about the proof of convergen
ce of the numerical scheme to global minimizers provided conditions of wel
l-preparation of the initial datum. The proof combines the previous result
s of mean-field limit with a novel asymptotic analysis\, and classical con
vergence results of numerical methods for SDE. We present several numerica
l experiments\, which show that the algorithm scales well with the dimensi
on and is extremely versatile. To quantify the performances of the new app
roach\, we show that the algorithm is able to perform essentially as good
as ad hoc state of the art methods and in some instances it obtains quanti
fiable better results in challenging problems in signal processing and mac
hine learning\, namely the phase retrieval problem and the robust subspace
detection.
LOCATION:Heinzel Seminar Room / Office Bldg West (I21.EG.101)\, IST Austria
ORGANIZER:chl@ist.ac.at
SUMMARY:Consensus-Based Optimization Over the Sphere: Theoretical Guarantee
s and Applications in Machine Learning
URL:https://talks-calendar.app.ist.ac.at/events/2502
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