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A Continuized View on Nesterov Acceleration

Raphaël Berthier 1, 2 Francis Bach 2, 1 Nicolas Flammarion 3 Pierre Gaillard 4 Adrien Taylor 2, 1
2 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique - ENS Paris, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
4 Thoth - Apprentissage de modèles à partir de données massives
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann
Abstract : We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradient steps at random times. This continuized variant benefits from the best of the continuous and the discrete frameworks: as a continuous process, one can use differential calculus to analyze convergence and obtain analytical expressions for the parameters; but a discretization of the continuized process can be computed exactly with convergence rates similar to those of Nesterov original acceleration. We show that the discretization has the same structure as Nesterov acceleration, but with random parameters.
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https://hal.archives-ouvertes.fr/hal-03138823
Contributor : Raphaël Berthier Connect in order to contact the contributor
Submitted on : Thursday, February 11, 2021 - 2:29:13 PM
Last modification on : Tuesday, January 11, 2022 - 11:16:05 AM
Long-term archiving on: : Wednesday, May 12, 2021 - 6:55:57 PM

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continuized.pdf
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Identifiers

  • HAL Id : hal-03138823, version 1
  • ARXIV : 2102.06035

Citation

Raphaël Berthier, Francis Bach, Nicolas Flammarion, Pierre Gaillard, Adrien Taylor. A Continuized View on Nesterov Acceleration. 2021. ⟨hal-03138823⟩

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