Geodesic
The exponential cost optimality for finite horizon semi-Markov decision processes
Kybernetika, Tome 58 (2022) no. 3, pp. 301-319.

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This paper considers an exponential cost optimality problem for finite horizon semi-Markov decision processes (SMDPs). The objective is to calculate an optimal policy with minimal exponential costs over the full set of policies in a finite horizon. First, under the standard regular and compact-continuity conditions, we establish the optimality equation, prove that the value function is the unique solution of the optimality equation and the existence of an optimal policy by using the minimum nonnegative solution approach. Second, we establish a new value iteration algorithm to calculate both the value function and the $\epsilon$-optimal policy. Finally, we give a computable machine maintenance system to illustrate the convergence of the algorithm.
DOI : 10.14736/kyb-2022-3-0301
Classification : 60E20, 90C40
Keywords: semi-Markov decision processes; exponential cost; finite horizon; optimality equation; optimal policy 
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Huo, Haifeng; Wen, Xian. The exponential cost optimality for finite horizon semi-Markov decision processes. Kybernetika, Tome 58 (2022) no. 3, pp. 301-319. doi : 10.14736/kyb-2022-3-0301. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2022-3-0301/

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