From Nesterov’s Estimate Sequence to Riemannian Acceleration

Kwangjun Ahn; Suvrit Sra

From Nesterov’s Estimate Sequence to Riemannian Acceleration

Kwangjun Ahn, Suvrit Sra

MIT Department of Electrical Engineering and Computer Science

Research output: Contribution to journal › Conference article › peer-review

34 Scopus citations

Abstract

We propose the first global accelerated gradient method for Riemannian manifolds. Toward establishing our results, we revisit Nesterov’s estimate sequence technique and develop a conceptually simple alternative from first principles. We then extend our analysis to Riemannian acceleration, localizing the key difficulty into “metric distortion.” We control this distortion via a novel geometric inequality, which enables us to formulate and analyze global Riemannian acceleration.

Original language	English
Pages (from-to)	84-118
Number of pages	35
Journal	Proceedings of Machine Learning Research
Volume	125
State	Published - 2020
Externally published	Yes
Event	33rd Conference on Learning Theory, COLT 2020 - Virtual, Online, Austria Duration: 9 Jul 2020 → 12 Jul 2020

Cite this

@article{74542e0df86948578f1ea955b79647cb,

title = "From Nesterov{\textquoteright}s Estimate Sequence to Riemannian Acceleration",

abstract = "We propose the first global accelerated gradient method for Riemannian manifolds. Toward establishing our results, we revisit Nesterov{\textquoteright}s estimate sequence technique and develop a conceptually simple alternative from first principles. We then extend our analysis to Riemannian acceleration, localizing the key difficulty into “metric distortion.” We control this distortion via a novel geometric inequality, which enables us to formulate and analyze global Riemannian acceleration.",

author = "Kwangjun Ahn and Suvrit Sra",

note = "Publisher Copyright: {\textcopyright} 2020 K. Ahn & S. Sra.; 33rd Conference on Learning Theory, COLT 2020 ; Conference date: 09-07-2020 Through 12-07-2020",

year = "2020",

language = "English",

volume = "125",

pages = "84--118",

journal = "Proceedings of Machine Learning Research",

issn = "2640-3498",

publisher = "ML Research Press",

}

TY - JOUR

T1 - From Nesterov’s Estimate Sequence to Riemannian Acceleration

AU - Ahn, Kwangjun

AU - Sra, Suvrit

PY - 2020

Y1 - 2020

N2 - We propose the first global accelerated gradient method for Riemannian manifolds. Toward establishing our results, we revisit Nesterov’s estimate sequence technique and develop a conceptually simple alternative from first principles. We then extend our analysis to Riemannian acceleration, localizing the key difficulty into “metric distortion.” We control this distortion via a novel geometric inequality, which enables us to formulate and analyze global Riemannian acceleration.

AB - We propose the first global accelerated gradient method for Riemannian manifolds. Toward establishing our results, we revisit Nesterov’s estimate sequence technique and develop a conceptually simple alternative from first principles. We then extend our analysis to Riemannian acceleration, localizing the key difficulty into “metric distortion.” We control this distortion via a novel geometric inequality, which enables us to formulate and analyze global Riemannian acceleration.

UR - http://www.scopus.com/inward/record.url?scp=85131585510&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:85131585510

SN - 2640-3498

VL - 125

SP - 84

EP - 118

JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

T2 - 33rd Conference on Learning Theory, COLT 2020

Y2 - 9 July 2020 through 12 July 2020

ER -

From Nesterov’s Estimate Sequence to Riemannian Acceleration

Abstract

Other files and links

Fingerprint

Cite this