Composite objective mirror descent

John C. Duchi; Shai Shalev-Shwartz; Yoram Singer; Ambuj Tewari

Composite objective mirror descent

John C. Duchi, Shai Shalev-Shwartz, Yoram Singer, Ambuj Tewari

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We present a new method for regularized convex optimization and analyze it under both online and stochastic optimization settings. In addition to unifying previously known firstorder algorithms, such as the projected gradient method, mirror descent, and forward-backward splitting, our method yields new analysis and algorithms. We also derive specific instantiations of our method for commonly used regularization functions, such as l₁, mixed norm, and trace-norm.

Original language	English (US)
Title of host publication	COLT 2010 - The 23rd Conference on Learning Theory
Pages	14-26
Number of pages	13
State	Published - Dec 1 2010
Externally published	Yes
Event	23rd Conference on Learning Theory, COLT 2010 - Haifa, Israel Duration: Jun 27 2010 → Jun 29 2010

Publication series

Name	COLT 2010 - The 23rd Conference on Learning Theory

Other

Other	23rd Conference on Learning Theory, COLT 2010
Country	Israel
City	Haifa
Period	6/27/10 → 6/29/10

All Science Journal Classification (ASJC) codes

Education

Cite this

@inproceedings{7340f8c0f616462389032ce3635ea0bb,

title = "Composite objective mirror descent",

abstract = "We present a new method for regularized convex optimization and analyze it under both online and stochastic optimization settings. In addition to unifying previously known firstorder algorithms, such as the projected gradient method, mirror descent, and forward-backward splitting, our method yields new analysis and algorithms. We also derive specific instantiations of our method for commonly used regularization functions, such as l1, mixed norm, and trace-norm.",

author = "Duchi, {John C.} and Shai Shalev-Shwartz and Yoram Singer and Ambuj Tewari",

year = "2010",

month = dec,

day = "1",

language = "English (US)",

isbn = "9780982252925",

series = "COLT 2010 - The 23rd Conference on Learning Theory",

pages = "14--26",

booktitle = "COLT 2010 - The 23rd Conference on Learning Theory",

note = "23rd Conference on Learning Theory, COLT 2010 ; Conference date: 27-06-2010 Through 29-06-2010",

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T1 - Composite objective mirror descent

AU - Duchi, John C.

AU - Shalev-Shwartz, Shai

AU - Singer, Yoram

AU - Tewari, Ambuj

PY - 2010/12/1

Y1 - 2010/12/1

N2 - We present a new method for regularized convex optimization and analyze it under both online and stochastic optimization settings. In addition to unifying previously known firstorder algorithms, such as the projected gradient method, mirror descent, and forward-backward splitting, our method yields new analysis and algorithms. We also derive specific instantiations of our method for commonly used regularization functions, such as l1, mixed norm, and trace-norm.

AB - We present a new method for regularized convex optimization and analyze it under both online and stochastic optimization settings. In addition to unifying previously known firstorder algorithms, such as the projected gradient method, mirror descent, and forward-backward splitting, our method yields new analysis and algorithms. We also derive specific instantiations of our method for commonly used regularization functions, such as l1, mixed norm, and trace-norm.

UR - http://www.scopus.com/inward/record.url?scp=84898075653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898075653&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84898075653

SN - 9780982252925

T3 - COLT 2010 - The 23rd Conference on Learning Theory

SP - 14

EP - 26

BT - COLT 2010 - The 23rd Conference on Learning Theory

T2 - 23rd Conference on Learning Theory, COLT 2010

Y2 - 27 June 2010 through 29 June 2010

ER -