Unifying mirror descent and dual averaging

Anatoli Juditsky; Joon Kwon; Éric Moulines

doi:10.1007/s10107-022-01850-3

Unifying mirror descent and dual averaging

Anatoli Juditsky
, Joon Kwon
, Éric Moulines

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce and analyze a new family of first-order optimization algorithms which generalizes and unifies both mirror descent and dual averaging. Within the framework of this family, we define new algorithms for constrained optimization that combines the advantages of mirror descent and dual averaging. Our preliminary simulation study shows that these new algorithms significantly outperform available methods in some situations.

Original language	English
Pages (from-to)	793-830
Number of pages	38
Journal	Mathematical Programming
Volume	199
Issue number	1-2
DOIs	https://doi.org/10.1007/s10107-022-01850-3
Publication status	Published - 1 May 2023

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title = "Unifying mirror descent and dual averaging",

abstract = "We introduce and analyze a new family of first-order optimization algorithms which generalizes and unifies both mirror descent and dual averaging. Within the framework of this family, we define new algorithms for constrained optimization that combines the advantages of mirror descent and dual averaging. Our preliminary simulation study shows that these new algorithms significantly outperform available methods in some situations.",

author = "Anatoli Juditsky and Joon Kwon and {\'E}ric Moulines",

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AB - We introduce and analyze a new family of first-order optimization algorithms which generalizes and unifies both mirror descent and dual averaging. Within the framework of this family, we define new algorithms for constrained optimization that combines the advantages of mirror descent and dual averaging. Our preliminary simulation study shows that these new algorithms significantly outperform available methods in some situations.

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Unifying mirror descent and dual averaging

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