scholarly journals Singularly perturbed linear programs and Markov decision processes

2016 ◽  
Vol 44 (3) ◽  
pp. 297-301
Author(s):  
Konstantin Avrachenkov ◽  
Jerzy A. Filar ◽  
Vladimir Gaitsgory ◽  
Andrew Stillman
Keyword(s):  
Markov Decision Processes ◽  
Decision Processes ◽  
Singularly Perturbed ◽  
Linear Programs ◽  
Markov Decision

scholarly journals Absorbing Continuous-Time Markov Decision Processes with Total Cost Criteria

2013 ◽  
Vol 45 (2) ◽  
pp. 490-519 ◽  
Author(s):  
Xianping Guo ◽  
Mantas Vykertas ◽  
Yi Zhang
Keyword(s):  
Markov Decision Processes ◽  
Optimal Policy ◽  
Continuous Time ◽  
Strong Duality ◽  
Performance Measure ◽  
Decision Processes ◽  
Linear Programs ◽  
Constrained Problems ◽  
Markov Decision ◽  
Unconstrained Problem

In this paper we study absorbing continuous-time Markov decision processes in Polish state spaces with unbounded transition and cost rates, and history-dependent policies. The performance measure is the expected total undiscounted costs. For the unconstrained problem, we show the existence of a deterministic stationary optimal policy, whereas, for the constrained problems with N constraints, we show the existence of a mixed stationary optimal policy, where the mixture is over no more than N+1 deterministic stationary policies. Furthermore, the strong duality result is obtained for the associated linear programs.

scholarly journals Absorbing Continuous-Time Markov Decision Processes with Total Cost Criteria

2013 ◽  
Vol 45 (02) ◽  
pp. 490-519 ◽  
Author(s):  
Xianping Guo ◽  
Mantas Vykertas ◽  
Yi Zhang
Keyword(s):  
Markov Decision Processes ◽  
Optimal Policy ◽  
Continuous Time ◽  
Strong Duality ◽  
Performance Measure ◽  
Decision Processes ◽  
Linear Programs ◽  
Constrained Problems ◽  
Markov Decision ◽  
Unconstrained Problem

In this paper we study absorbing continuous-time Markov decision processes in Polish state spaces with unbounded transition and cost rates, and history-dependent policies. The performance measure is the expected total undiscounted costs. For the unconstrained problem, we show the existence of a deterministic stationary optimal policy, whereas, for the constrained problems withNconstraints, we show the existence of a mixed stationary optimal policy, where the mixture is over no more thanN+1 deterministic stationary policies. Furthermore, the strong duality result is obtained for the associated linear programs.

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