0369603 20240103200059.220120109235959.9 2310 Praha ÚTIA AV ČR, v.v.i 2011 14 s. Research Report 2310 HDMR approximation Bellman equation minimization of HDMR functions cav_un_auth*0234872 Pištěk Miroslav Adaptivní systémy Department of Adaptive Systems AS AS UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2012/AS/pistek-approximate dynamic programming based on high dimensional model representation.pdf GAP102/11/0437 GA ČR CZ cav_un_auth*0273082 CEZ:AV0Z10750506 In this article, an efficient algorithm for an optimal decision strategy approximation is introduced. The proposed approximation of the Bellman equation is based on HDMR technique. This non-parametric function approximation is used not only to reduce memory demands necessary to store Bellman function, but also to allow its fast approximate minimization. On that account, a clear connection between HDMR minimization and discrete optimization is newly established. In each time step of the backward evaluation of the Bellman function, we relax the parameterized discrete minimization subproblem to obtain parameterized trust region problem. We observe that the involved matrix is the same for all parameters owning to the structure of HDMR approximation. We find eigenvalue decomposition of this matrix to solve all trust region problems effectively. 2012 BC 1 4 O 4o 20231122134831.9 http://hdl.handle.net/11104/0203627 2011 Soubory v repozitáři: 0369603.pdf 2011 Praha ÚTIA AV ČR, v.v.i