<div class="csl-bib-body">
<div class="csl-entry">Aubin, P.-C. (2024, June 7). <i>Alternating minimization and gradient descent with c(x,y) cost</i> [Conference Presentation]. One World Optimization Seminar in Vienna, Wien, Austria.</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/198023
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dc.description.abstract
How to go beyond the quadratic cost in optimization? Through Bregman divergences? Can we go beyond and non-Euclidean? I will show that by replacing the quadratic or Bregman regularizer with a general cost function c(x,y) and using a majorize-minimize framework we obtain a generic class of algorithms encompassing mirror/natural/Riemannian gradient descent by reframing them as an alternating minimization, each for a different cost c(x,y). We prove that a five-point property inspired from [Csiszár and Tusnady 1984] provides (sub)linear rates, extending the known theory of (relative) smoothness and convexity, and incorportating them into c-concavity and cross-convexity. Both notions are connected with the theory of cross-curvature in optimal transport and give a new spin to studying global convergence rates, e.g. for Newton method, in a systematic manner.This is a joint work with Flavien Léger (INRIA Paris) https://arxiv.org/abs/2305.04917
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.subject
Optimization
en
dc.subject
Gradient Descent
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dc.subject
Convexity
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dc.title
Alternating minimization and gradient descent with c(x,y) cost
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.relation.grantno
P 36344N
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dc.type.category
Conference Presentation
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tuw.publication.invited
invited
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tuw.project.title
Unilateralität und Asymmetrie in der Variationsanalyse
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tuw.researchTopic.id
C4
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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tuw.event.name
One World Optimization Seminar in Vienna
en
tuw.event.startdate
03-06-2024
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tuw.event.enddate
07-06-2024
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Wien
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tuw.event.country
AT
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tuw.event.institution
Universität Wien
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tuw.event.presenter
Aubin, Pierre-Cyril
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tuw.event.track
Single Track
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.openairetype
conference paper not in proceedings
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item.languageiso639-1
en
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.grantfulltext
none
-
item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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crisitem.project.funder
FWF - Österr. Wissenschaftsfonds
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crisitem.project.grantno
P 36344N
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crisitem.author.dept
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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crisitem.author.parentorg
E105 - Institut für Stochastik und Wirtschaftsmathematik
