TARU PUBLICATIONS
Journal of Information and Optimization Sciences cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

Powered by:Powered by

Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

Issues up to 2022 co-published with and available at:Taylor & Francis
submissions@tarupublications.com
Open Access Research Article

A discrete time Markov decision process under a fractional discounted reward criterion

*

* Corresponding author · click or hover a name for details

pp. 1237–1247Vol. 47Issue 4April 2026DOI: 10.47974/JIOS-1329XML
Received:
08 Jun 2022
Accepted:
09 Nov 2022
Published Online:
02 Feb 2026
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1329
Pages:
1237–1247

Abstract

We consider a discrete-time Markov decision process with a state space and an action space in general setting, evaluated according to a fractional discounting reward criterion. For the sake of discussing an optimal control for this model, we transform this model to a Markov decision model under the usual discounted reward criterion by using the parametric method. We discuss the existence of an optimal policy as well as the continuity of the corresponding optimal value function for our model.

Keywords

Subject Classifications

90C3990C4093E20

References

[1] Vijay Kumar Aggarwal, Ramaswamy Chandrasekaran, and Kunhiraman P. K. Nair, “Markov ratio decision processes,” Journal of Optimization Theory and Applications, vol. 21, pp. 27–37 (1977).
[2] Dimitri P. Bertsekas and Steven E. Shreve, Stochastic Optimal Control. New York, NY, USA: Academic Press (1978).
[3] Onesimo Hernández-Lerma, Adaptive Markov Control Processes. New York, NY, USA: Springer-Verlag (1989).
[4] Onesimo Hernández-Lerma and Jean Bernard Lasserre, Discrete-Time Markov Control Processes. New York, NY, USA: Springer-Verlag (1996).
[5] Seiichi Iwamoto and Toshiharu Fujita, “Markov decision processes under fractional criterions,” Kyoto University RIMS Kokyuroku, no. 1079, pp. 153–163 (1999) (in Japanese).
[6] Krisorn Jittorntrum, “An implicit function theorem,” Journal of Optimization Theory and Applications, vol. 25, pp. 575–577 (1978).
[7] Hang-Chin Lai, “On a dynamic fractional game,” Kyoto University RIMS Kokyuroku, no. 1298, pp. 151–160 (2002).
[8] Hiroaki Morimoto, “On average cost stopping time problems,” Probability Theory and Related Fields, vol. 90, pp. 469–490 (1991).
[9] Masamitsu Ohnishi, “Optimal minimal-repair and replacement problem under average cost criterion: Optimality of(t,T)-policy,” Journal of the Operations Research Society of Japan, vol. 40, pp. 373–389 (1997).
[10] Martin L. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming. New York, NY, USA: Wiley-Interscience (1994).
[11] Zhiyuan Ren and Bruce Krogh, “Markov decision processes with fractional costs,” IEEE Transactions on Automatic Control, vol. 50, pp. 646–650 (2005).
[12] Yoichi Sawasaki, Yutaka Kimura, and Kensuke Tanaka, “A two-person zero-sum game with fractional loss function,” Journal of the Operations Research Society of Japan, vol. 43, pp. 209–218 (2000).
[13] Maurice Robin, “On some impulse control problems with long run average cost,” SIAM Journal on Control and Optimization, vol. 19, pp. 333–358 (1981).
[14] Ioan Mihai Stancu-Minasian, Fractional Programming. Dordrecht, The Netherlands: Kluwer Academic Publishers (1997).
[15] Lukasz Stettner, “On some stopping impulse control problems with a general discount rate criteria,” Probability and Mathematical Statistics, vol. 10, pp. 223–245 (1989).
[16] Min Sun, “An optimal stopping time problem with time average cost in a bounded interval,” Systems & Control Letters, vol. 8, pp. 173–180 (1986).
[17] Min Sun, “A multidimensional optimal stopping-time problem with time-average criterion,” Optimal Control Applications and Methods, vol. 11, pp. 85–93 (1990).
[18] Teruo Tanaka, “A partially observable discrete-time Markov decision process with a fractional discounted reward,” Journal of Information and Optimization Sciences, vol. 38, no. 1, pp. 21–37 (2017).
[19] Qi Wang, Masayuki Kageyama, and Jingyao Zhang, “New evaluation criteria in the Markov decision processes,” Journal of Statistics and Management Systems, vol. 24, no. 3, pp. 625–632 (2021).

Views: 150Downloads: 73Citations: 0