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Weighted Markov decision processes with perturbation
Liu, K; Filar, JA
AbstractIn this paper we consider the weighted reward Markov decision process, with perturbation. The "weighted reward" refers to appropriately normalized convex combination of the discounted and the long-run average reward criteria. This criterion allows the controller to trade-off short-term costs versus long-term costs. In every application where both the discounted and the long-run average criteria have been proposed in the past, there is clearly a rationale for considering the weighted criterion. Of course, as with all Markov decision models, the standard weighted criterion model assumes that all the transition probabilities are known precisely. Since, in most applications this would not be the case, we consider the perturbed version of the weighted reward model. We prove that in most cases a nearly optimal control can be found in the class of relatively simple "ultimately deterministic" controls. These are controls which behave just like deterministic stationary controls, after a certain point of time.
KeywordMarkov decision processes weighted reward optimal policy delta-optimal singular perturbation general perturbation
WOS Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000170339000009
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Document Type期刊论文
Corresponding AuthorLiu, K
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
2.Univ S Australia, Sch Math, Adelaide, SA 5095, Australia
Recommended Citation
GB/T 7714
Liu, K,Filar, JA. Weighted Markov decision processes with perturbation[J]. MATHEMATICAL METHODS OF OPERATIONS RESEARCH,2001,53(3):465-480.
APA Liu, K,&Filar, JA.(2001).Weighted Markov decision processes with perturbation.MATHEMATICAL METHODS OF OPERATIONS RESEARCH,53(3),465-480.
MLA Liu, K,et al."Weighted Markov decision processes with perturbation".MATHEMATICAL METHODS OF OPERATIONS RESEARCH 53.3(2001):465-480.
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