Some advances on constrained Markov decision processes in Borel spaces with random state-dependent discount factors

References

• Carmon Y, Shwartz A. Markov decision processes with exponentially representable discounting. Oper Res Lett. 2009;37:51–55.
   Web of Science ®Google Scholar
• Feinberg EA, Shwartz A. Markov decision models with weighted discounted criteria. Math Oper Res. 1994;19:152–168.
   Web of Science ®Google Scholar
• Hinderer K. Foundations of non-stationary dynamic programming with discrete-time parameter. Berlin: Springer-Verlag; 1970. (Lecture Notes Oper. Res. Math. Syst.; 33).
   Google Scholar
• Jasso-Fuentes H, Menaldi JL, Prieto-Rumeau T. Discrete-time control with non-constant discount factor. Math Meth Oper Res. 2020;92:377–399.
   Web of Science ®Google Scholar
• Minjárez-Sosa JA. Markov control models with unknown random state-action-dependent discount factors. TOP. 2015;23:743–772.
   Web of Science ®Google Scholar
• Schäl M. Conditions for optimality and for the limit of n-stage optimal policies to be optimal. Z Wahrs Verw Gerb. 1975;32:179–196.
   Web of Science ®Google Scholar
• Wei Q, Guo X. Markov decision processes with state-dependent discount factors and unbounded rewards/costs. Oper Res Lett. 2011;39:369–374.
   Web of Science ®Google Scholar
• González-Hernández J, López-Martínez RR, Pérez-Hernández R. Markov control processes with randomized discounted cost in Borel space. Math Meth Oper Res. 2007;65:27–44.
   Web of Science ®Google Scholar
• González-Hernández J, López-Martínez RR, Minjárez-Sosa JA. Adaptive policies for stochastic systems under a randomized discounted criterion. Bol Soc Mat Mex. 2008;14:149–163.
   Google Scholar
• González-Hernández J, López-Martínez RR, Minjárez-Sosa JA. Approximation, estimation and control of stochastic systems under a randomized discounted cost criterion. Kybernetika. 2009;45:737–754.
   Web of Science ®Google Scholar
• González-Hernández J, López-Martínez RR, Minjárez-Sosa JA, et al. Constrained Markov control processes with randomized discounted cost criteria: occupation measures and extremal points. Risk and Decision Analysis. 2013;4:163–176.
   Google Scholar
• González-Hernández J, López-Martínez RR, Minjárez-Sosa JA, et al. Constrained Markov control processes with randomized discounted rate: infinite linear programming approach. Optim Control Appl Meth. 2014;35:575–591.
   Web of Science ®Google Scholar
• Altman E. Constrained Markov decision processes with total cost criteria: occupation measures and primal LP. Math Meth Oper Res. 1996;43:45–72.
   Google Scholar
• Alvarez-Mena J, Hernández-Lerma O. Convergence of the optimal values of constrained Markov control processes. Math Meth Oper Res. 2002;55(3):461–484.
   Web of Science ®Google Scholar
• Guo XP. Constrained nonhomogeneous Markov decision processes with expected total reward criterion. Acta Appl Math Sin (English Ser). 2000;23:230–235.
   Google Scholar
• Hernández-Lerma O, González-Herná ndez J, López-Martínez RR. Constrained average cost Markov control processes in Borel spaces. SIAM J Control Optim. 2003;42:442–468.
   Web of Science ®Google Scholar
• Jasso-Fuentes H, Menndoza-Pérez AF de-la-Cruz-Courtois OA. Constrained Markov decision processes in Borel spaces: from discounted to average optimality. Math Meth Oper Res. 2016;84:489–525.
   Web of Science ®Google Scholar
• Piunovskiy AB. Optimal control of random sequences in problems with constraints. Dordrecht: Kluwer; 1997.
   Google Scholar
• Hernández-Lerma O, Lasserre JB. Discrete-time Markov control processes: basic optimality criteria. New York: Springer-Verlag; 1996.
   Google Scholar
• Hernández-Lerma O, Lasserre JB. Further topics on discrete-time Markov control processes. New York: Springer-Verlag; 1999.
   Google Scholar
• Bertsekas DP, Shreve SE. Stochastic optimal control. New York: Academic Press; 1978.
   Google Scholar
• Dynkin EB, Yushkevich AA. Controlled Markov processes. Berlin: Springer-Verlag; 1979.
   Google Scholar
• Billingsley P. Convergence of probability measures. New York: Wileym; 1968.
   Google Scholar
• Bourbaki N. Integration, chap. IX. Paris: Hermann; 1969.
   Google Scholar
• Luenberger DG. Optimization by vector space methods. New York: Wiley; 1969.
   Google Scholar
• Hernández-Lerma O, Romera R. The scalarization approach to multiobjective Markov control problems: why does it work? Appl Math Optim. 2004;50:279–293.
   Web of Science ®Google Scholar