| Presentation | 2016-11-16 Proximal Average Accelerated Proximal Gradient Algorithm with Adaptive Restart Yoshihiro Nakazato, Kazuto Fukuchi, Jun Sakuma, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(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) |
| Keyword(in English) | Convex Optimization / Composite Sparse Regularizers |
| Paper # | IBISML2016-55 |
| Date of Issue | 2016-11-09 (IBISML) |
| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2016/11/16(3days) |
| 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) |
| Chair | Kenji Fukumizu(ISM) |
| Vice Chair | Masashi Sugiyama(Univ. of Tokyo) / Hisashi Kashima(Kyoto Univ.) |
| Secretary | Masashi Sugiyama(Univ. of Tokyo) / Hisashi Kashima(Nagoya Inst. of Tech.) |
| Assistant | Toshihiro Kamishima(AIST) / Tomoharu Iwata(NTT) |
| Paper Information | |
| Registration To | Technical Committee on Infomation-Based Induction Sciences and Machine Learning |
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| Language | JPN |
| 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 |
| 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) |
| Date | 2016-11-16 |
| Paper # | IBISML2016-55 |
| Volume (vol) | vol.116 |
| Number (no) | IBISML-300 |
| Page | pp.pp.65-71(IBISML), |
| #Pages | 7 |
| Date of Issue | 2016-11-09 (IBISML) |