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Paper Abstract and Keywords
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
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.
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
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 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  
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 
Date of Issue 2012-03-05 (IBISML) 

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