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First Passage Models for Denumerable Semi-Markov Decision Processes with Nonnegative Discounted Costs
Yonghui Huang * #,Guo Xianping
Sun Yat-Sen University
*Correspondence author
#Submitted by
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Funding: 国家自然科学基金（No.60874004）
Opened online:12 January 2009
Accepted by: none
Citation: Yonghui Huang,Guo Xianping.First Passage Models for Denumerable Semi-Markov Decision Processes with Nonnegative Discounted Costs[OL]. [12 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27677
 
 
This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs. The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set. We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy. Then, we prove that the value function satisfies the optimality equation and there exists an optimal (or $\\epsilon$-optimal) stationary policy under suitable conditions by using a minimum nonnegative solution approach, and further we give some properties of optimal policies.In addition, a value iteration algorithm for computing the value function and optimal policies is developed and an example is given. Finally, it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.
Keywords:Semi-Markov decision processes;target set;first
 
 
 

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