Convergence of Controlled Models for Continuous-Time Markov Decision Processes with Constrained Average Criteria
Year: 2019
Author: Wenzhao Zhang, Xianzhu Xiong
Annals of Applied Mathematics, Vol. 35 (2019), Iss. 4 : pp. 449–464
Abstract
This paper attempts to study the convergence of optimal values and optimal policies of continuous-time Markov decision processes (CTMDP for short) under the constrained average criteria. For a given original model $\mathcal{M}$$∞$ of CTMDP with denumerable states and a sequence {$\mathcal{M}$$n$} of CTMDP with finite states, we give a new convergence condition to ensure that the optimal values and optimal policies of {$\mathcal{M}$$n$} converge to the optimal value and optimal policy of $\mathcal{M}$$∞$ as the state space $S$$n$ of $\mathcal{M}$$n$ converges to the state space $S$$∞$ of $\mathcal{M}$$∞$, respectively. The transition rates and cost/reward functions of $\mathcal{M}$$∞$ are allowed to be unbounded. Our approach can be viewed as a combination method of linear program and Lagrange multipliers.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-AAM-18090
Annals of Applied Mathematics, Vol. 35 (2019), Iss. 4 : pp. 449–464
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: continuous-time Markov decision processes optimal value optimal policies constrained average criteria occupation measures.