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Paper Abstract and Keywords
Presentation 2016-11-16 15:00
Proximal Average Accelerated Proximal Gradient Algorithm with Adaptive Restart
Yoshihiro Nakazato, Kazuto Fukuchi, Jun Sakuma (Univ. Tsukuba) IBISML2016-55
Abstract (in Japanese) (See Japanese page) 
(in English) When using multiple regularizers, their proximal mapping is not easily available in closed form.
The method to calculate proximal mapping of multiple regularizers needs many calculating cost.
When the regularizers satisfy some certain conditioncite{yu2013decomposing}cite{martins2011online}, there are optimization methods to solve multiple sparse regularization problem.
But their condition is not always satisfied.
There are some approximation method for multiple regularizers: smoothingcite{nesterov2005smooth}, proximal averagecite{yu2013better}.
Yu showed that by using proximal average and FISTA, $O(1/sqrt{epsilon})$ iteration is needed for $epsilon$-optimal.
In this research, when the average of the square of Lipschitz constant of regularizers is larger than the Lipschitz constant of the gradient of the loss function, we show that the Algorithm proximal average accelerated proximal gradient(PA-APG) is as slow as $1/epsilon$.
And, we propose new algorithm which is faster than PA-APG.
Keyword (in Japanese) (See Japanese page) 
(in English) Convex Optimization / Composite Sparse Regularizers / / / / / /  
Reference Info. IEICE Tech. Rep., vol. 116, no. 300, IBISML2016-55, pp. 65-71, Nov. 2016.
Paper # IBISML2016-55 
Date of Issue 2016-11-09 (IBISML) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
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reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee IBISML  
Conference Date 2016-11-16 - 2016-11-18 
Place (in Japanese) (See Japanese page) 
Place (in English) Kyoto Univ. 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Information-Based Induction Science Workshop (IBIS2016) 
Paper Information
Registration To IBISML 
Conference Code 2016-11-IBISML 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Proximal Average Accelerated Proximal Gradient Algorithm with Adaptive Restart 
Sub Title (in English)  
Keyword(1) Convex Optimization  
Keyword(2) Composite Sparse Regularizers  
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1st Author's Name Yoshihiro Nakazato  
1st Author's Affiliation University of Tsukuba (Univ. Tsukuba)
2nd Author's Name Kazuto Fukuchi  
2nd Author's Affiliation University of Tsukuba (Univ. Tsukuba)
3rd Author's Name Jun Sakuma  
3rd Author's Affiliation University of Tsukuba (Univ. Tsukuba)
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Speaker Author-1 
Date Time 2016-11-16 15:00:00 
Presentation Time 180 minutes 
Registration for IBISML 
Paper # IBISML2016-55 
Volume (vol) vol.116 
Number (no) no.300 
Page pp.65-71 
#Pages 7 
Date of Issue 2016-11-09 (IBISML) 

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