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Title:	非均質馬可夫決策過程在演算法上的一些數學性質
Other Titles:	Reviewing Some Mathematical Properties of Algorithms in Npnhomogeneous Markov Decision Processes
Authors:	劉任昌 Liou,Chen-Chang 陸行 Luh,Hsing
Contributors:	應數系
Keywords:	非均質馬可夫決策過程;預測期数;動態規劃;縮收函數;超平面行数函数 Nonhomogeneous Markov Decision Processes;Forecast Horizon;Dynamic Programming;Contraction Mapping;Affine Mapping
Date:	1999-11
Issue Date:	2008-12-24 13:31:40 (UTC+8)
Abstract:	Hopp, Bean and Duenyas (1992) formulated a mixed integer program (MIP) to determine whether a finite time horizon is a forecast horizon in a nonhomogeneous Markov decision process (NMDP). Their formula is provided by complex Bender`s decomposition techniques. In this paper, we investigate in details of the contraction property and affine mapping property of NMDP, By these properties, Hopp et al.`s formula is relicvcd of the complex MIP formula and Bender`s decomposition algorithm. We only need to check a finite number of vertices at a polyhedral set shaped by the solution of the NMDP. The analysis gives insight into the NMDP and facilitates the process in detcnnining the forecast horizon. Furthermore, this NMDP formulation is presented in the form of a simple dynamic function which is different from the linear program presented by Hopp et al.
Relation:	工業工程學刊,16(6),711-724
Data Type:	article
Appears in Collections:	[Department of Mathematical Sciences] Periodical Articles

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