TY - GEN
T1 - A Fixed-Point Analysis of Regularized Dual Averaging under Static Scenarios
AU - Yukawa, Masahiro
AU - Yamada, Isao
N1 - Funding Information:
ACKNOWLEDGMENT This work was supported in part by JSPS Grants-in-Aids (18H01446, 15K13986, 15H02757).
Publisher Copyright:
© 2018 APSIPA organization.
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.
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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.
T2 - 10th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2018
Y2 - 12 November 2018 through 15 November 2018
ER -