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dc.contributor.author
Bécigneul, Gary
dc.contributor.author
Ganea, Octavian-Eugen
dc.date.accessioned
2024-06-10T13:45:41Z
dc.date.available
2020-01-24T17:26:19Z
dc.date.available
2020-01-30T12:12:33Z
dc.date.available
2024-06-10T13:45:41Z
dc.date.issued
2023-05
dc.identifier.isbn
978-1-7138-7273-3
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/393955
dc.description.abstract
Several first order stochastic optimization methods commonly used in the Euclidean domain such as stochastic gradient descent (SGD), accelerated gradient descent or variance reduced methods have already been adapted to certain Riemannian settings. However, some of the most popular of these optimization tools - namely Adam , Adagrad and the more recent Amsgrad - remain to be generalized to Riemannian manifolds. We discuss the difficulty of generalizing such adaptive schemes to the most agnostic Riemannian setting, and then provide algorithms and convergence proofs for geodesically convex objectives in the particular case of a product of Riemannian manifolds, in which adaptivity is implemented across manifolds in the cartesian product. Our generalization is tight in the sense that choosing the Euclidean space as Riemannian manifold yields the same algorithms and regret bounds as those that were already known for the standard algorithms. Experimentally, we show faster convergence and to a lower train loss value for Riemannian adaptive methods over their corresponding baselines on the realistic task of embedding the WordNet taxonomy in the Poincare ball.
en_US
dc.language.iso
en
en_US
dc.publisher
Curran
en_US
dc.title
Riemannian Adaptive Optimization Methods
en_US
dc.type
Conference Paper
ethz.book.title
International Conference on Learning Representations (ICLR 2019)
en_US
ethz.journal.volume
9
en_US
ethz.pages.start
6384
en_US
ethz.pages.end
6399
en_US
ethz.event
7th International Conference on Learning Representations (ICLR 2019)
en_US
ethz.event.location
New Orleans, LA, USA
en_US
ethz.event.date
May 6-9, 2019
en_US
ethz.notes
Conference lecture held on May 8, 2019.
en_US
ethz.publication.place
Red Hook, NY
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02150 - Dep. Informatik / Dep. of Computer Science::02661 - Institut für Maschinelles Lernen / Institute for Machine Learning::09462 - Hofmann, Thomas / Hofmann, Thomas
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02150 - Dep. Informatik / Dep. of Computer Science::02661 - Institut für Maschinelles Lernen / Institute for Machine Learning::09462 - Hofmann, Thomas / Hofmann, Thomas
en_US
ethz.relation.isNewVersionOf
https://openreview.net/forum?id=r1eiqi09K7
ethz.relation.isNewVersionOf
https://doi.org/10.48550/arXiv.1810.00760
ethz.date.deposited
2020-01-24T17:26:30Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2020-01-30T12:12:43Z
ethz.rosetta.lastUpdated
2020-01-30T12:12:43Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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