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| Presentation | 2012-03-12 14:40 Kernel Bellman Equations in POMDPs Yu Nishiyama (ISM), Abdeslam Boularias (MPI), Arthur Gretton (UCL), Kenji Fukumizu (ISM)  IBISML2011-92 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | We propose to handle POMDPs in reproducing kernel Hilbert spaces (RKHSs) using recent kernel methods of embedding distributions in an RKHS and kernel Bayes rule (KBR). We embed Bellman equations to equations over an RKHS on the set of states and define value functions as functions over the RKHS. We then learn a policy as a mapping from elements of the RKHS to actions. We give empirical representations of the Bellman equations and use it for value iteration algorithms with the kernel Bayes rule. In experiments, we demonstrate the kernel value iteration with finite horizons on some benchmarks in POMDPs and show that the policy converged to the policy that the exact model computed. We also propose QMDP approximations with this kernel methods for the setting of initial values and for pruning action edges to make computationally efficient. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | POMDP / RKHS / Distribution Embeddings / Value Iteration / QMDP / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 111, no. 480, IBISML2011-92, pp. 35-42, March 2012. | |
| Paper # | IBISML2011-92 | |
| Date of Issue | 2012-03-05 (IBISML) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and 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) | |
| Download PDF | IBISML2011-92 |
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| Conference Information | |
| Committee | IBISML |
| Conference Date | 2012-03-12 - 2012-03-13 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | The Institute of Statistical Mathematics |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Mathematical Statistics, Databases, etc. |
| Paper Information | |
| Registration To | IBISML |
| Conference Code | 2012-03-IBISML |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Kernel Bellman Equations in POMDPs |
| Sub Title (in English) | |
| Keyword(1) | POMDP |
| Keyword(2) | RKHS |
| Keyword(3) | Distribution Embeddings |
| Keyword(4) | Value Iteration |
| Keyword(5) | QMDP |
| Keyword(6) | |
| Keyword(7) | |
| Keyword(8) | |
| 1st Author's Name | Yu Nishiyama |
| 1st Author's Affiliation | The Institute of Statistical Mathematics (ISM) |
| 2nd Author's Name | Abdeslam Boularias |
| 2nd Author's Affiliation | Max Planck Institute (MPI) |
| 3rd Author's Name | Arthur Gretton |
| 3rd Author's Affiliation | University College London (UCL) |
| 4th Author's Name | Kenji Fukumizu |
| 4th Author's Affiliation | The Institute of Statistical Mathematics (ISM) |
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| Speaker | Author-1 |
| Date Time | 2012-03-12 14:40:00 |
| Presentation Time | 25 minutes |
| Registration for | IBISML |
| Paper # | IBISML2011-92 |
| Volume (vol) | vol.111 |
| Number (no) | no.480 |
| Page | pp.35-42 |
| #Pages | 8 |
| Date of Issue | 2012-03-05 (IBISML) |
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