Abstract
In this paper, we analyze the properties of a fixed point of a certain mapping that is implicitly used in each of the regularized dual averaging (RDA) and projection-based RDA (PDA) algorithms. It turns out that, if the loss function has a nonexpansive (1-Lipschltz) gradient such as in the case of a half squared-distance function, RDA converges to a minimizer of the penalized loss function under a restrictive condition. Meanwhile, the fixed point for PDA gives a minimizer of the 'unpenalized' loss function. Some simulation studies are also presented to support the theoretical findings.
| Original language | English |
|---|---|
| Title of host publication | 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 207-211 |
| Number of pages | 5 |
| ISBN (Electronic) | 9789881476852 |
| DOIs | |
| Publication status | Published - 2019 Mar 4 |
| Event | 10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Honolulu, United States Duration: 2018 Nov 12 → 2018 Nov 15 |
Publication series
| Name | 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings |
|---|
Conference
| Conference | 10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 |
|---|---|
| Country | United States |
| City | Honolulu |
| Period | 18/11/12 → 18/11/15 |
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ASJC Scopus subject areas
- Information Systems
Cite this
A Fixed-Point Analysis of Regularized Dual Averaging under Static Scenarios. / Yukawa, Masahiro; Yamada, Isao.
2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 207-211 8659576 (2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - A Fixed-Point Analysis of Regularized Dual Averaging under Static Scenarios
AU - Yukawa, Masahiro
AU - Yamada, Isao
PY - 2019/3/4
Y1 - 2019/3/4
N2 - In this paper, we analyze the properties of a fixed point of a certain mapping that is implicitly used in each of the regularized dual averaging (RDA) and projection-based RDA (PDA) algorithms. It turns out that, if the loss function has a nonexpansive (1-Lipschltz) gradient such as in the case of a half squared-distance function, RDA converges to a minimizer of the penalized loss function under a restrictive condition. Meanwhile, the fixed point for PDA gives a minimizer of the 'unpenalized' loss function. Some simulation studies are also presented to support the theoretical findings.
AB - In this paper, we analyze the properties of a fixed point of a certain mapping that is implicitly used in each of the regularized dual averaging (RDA) and projection-based RDA (PDA) algorithms. It turns out that, if the loss function has a nonexpansive (1-Lipschltz) gradient such as in the case of a half squared-distance function, RDA converges to a minimizer of the penalized loss function under a restrictive condition. Meanwhile, the fixed point for PDA gives a minimizer of the 'unpenalized' loss function. Some simulation studies are also presented to support the theoretical findings.
UR - http://www.scopus.com/inward/record.url?scp=85063503000&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85063503000&partnerID=8YFLogxK
U2 - 10.23919/APSIPA.2018.8659576
DO - 10.23919/APSIPA.2018.8659576
M3 - Conference contribution
AN - SCOPUS:85063503000
T3 - 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings
SP - 207
EP - 211
BT - 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
ER -