0399560 20240903170627.720131203235959.9 84889006605 000328665200004 18 s. P cav_un_epca*02971630023-5954495 (2013)720-737Ústav teorie informace a automatizace AV ČR, v. v. i. approximate dynamic programming Bellman equation approximate HDMR minimization trust region problem cav_un_auth*0234872 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Pištěk Miroslav UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2013/AS/pistek-0399560.pdf cav_un_auth*0273082 GAP102/11/0437 GA ČR CZ This article introduces an algorithm for implicit High Dimensional Model Representation (HDMR) of the Bellman equation. This approximation technique reduces memory demands of the algorithm considerably. Moreover, we show that HDMR enables fast approximate min- imization which is essential for evaluation of the Bellman function. In each time step, the problem of parametrized HDMR minimization is relaxed into trust region problems, all sharing the same matrix. Finding its eigenvalue decomposition, we effectively achieve estimates of all minima. Their full-domain representation is avoided by HDMR and then the same approach is used recursively in the next time step. An illustrative example of N-armed bandit problem is included. We assume that the newly established connection between approximate HDMR minimization and the trust region problem can be beneficial also to many other applications. BC 2014 4 O 4o 20231122135935.5 RVO:67985556 http://hdl.handle.net/11104/0226953 COMPUTERSCIENCECYBERNETICS 0.577 0.098 9.IV 0.00191 0.341 655 61 0.348 ScienceCitationIndexExpanded Q2 35.159 31.250 Q3 Q3 2013 Soubory v repozitáři: pistek-0399560.pdf 84889006605 SCOPUS 000328665200004 WOS cav_un_epca*0297163 Kybernetika 0023-5954 Roč. 49 č. 5 2013 720 737 Ústav teorie informace a automatizace AV ČR, v. v. i.