Solution to the optimality equation in a class of Markov decision chains with the average cost criterion
Rolando Cavazos-Cadena (1991)
Kybernetika
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Rolando Cavazos-Cadena (1991)
Kybernetika
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Zhu, Quanxin, Guo, Xianping (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Oscar Vega-Amaya, Fernando Luque-Vásquez (2000)
Applicationes Mathematicae
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We deal with semi-Markov control processes (SMCPs) on Borel spaces with unbounded cost and mean holding time. Under suitable growth conditions on the cost function and the mean holding time, together with stability properties of the embedded Markov chains, we show the equivalence of several average cost criteria as well as the existence of stationary optimal policies with respect to each of these criteria.
Oscar Vega-Amaya (1999)
Applicationes Mathematicae
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We study the existence of sample path average cost (SPAC-) optimal policies for Markov control processes on Borel spaces with strictly unbounded costs, i.e., costs that grow without bound on the complement of compact subsets. Assuming only that the cost function is lower semicontinuous and that the transition law is weakly continuous, we show the existence of a relaxed policy with 'minimal' expected average cost and that the optimal average cost is the limit of discounted programs. Moreover,...
Karel Sladký (2010)
Kybernetika
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In this note we focus attention on identifying optimal policies and on elimination suboptimal policies minimizing optimality criteria in discrete-time Markov decision processes with finite state space and compact action set. We present unified approach to value iteration algorithms that enables to generate lower and upper bounds on optimal values, as well as on the current policy. Using the modified value iterations it is possible to eliminate suboptimal actions and to identify an optimal...
Evgueni Gordienko, Onésimo Hernández-Lerma (1995)
Applicationes Mathematicae
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This paper considers discrete-time Markov control processes on Borel spaces, with possibly unbounded costs, and the long run average cost (AC) criterion. Under appropriate hypotheses on weighted norms for the cost function and the transition law, the existence of solutions to the average cost optimality inequality and the average cost optimality equation are shown, which in turn yield the existence of AC-optimal and AC-canonical policies respectively.