# Constrained Continuous-Time Markov Decision Processes on the Finite Horizon

Constrained Continuous-Time Markov Decision Processes on the Finite Horizon This paper studies the constrained (nonhomogeneous) continuous-time Markov decision processes on the finite horizon. The performance criterion to be optimized is the expected total reward on the finite horizon, while N constraints are imposed on similar expected costs. Introducing the appropriate notion of the occupation measures for the concerned optimal control problem, we establish the following under some suitable conditions: (a) the class of Markov policies is sufficient; (b) every extreme point of the space of performance vectors is generated by a deterministic Markov policy; and (c) there exists an optimal Markov policy, which is a mixture of no more than \$\$N+1\$\$ N + 1 deterministic Markov policies. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Constrained Continuous-Time Markov Decision Processes on the Finite Horizon

25 pages

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### Abstract

This paper studies the constrained (nonhomogeneous) continuous-time Markov decision processes on the finite horizon. The performance criterion to be optimized is the expected total reward on the finite horizon, while N constraints are imposed on similar expected costs. Introducing the appropriate notion of the occupation measures for the concerned optimal control problem, we establish the following under some suitable conditions: (a) the class of Markov policies is sufficient; (b) every extreme point of the space of performance vectors is generated by a deterministic Markov policy; and (c) there exists an optimal Markov policy, which is a mixture of no more than \$\$N+1\$\$ N + 1 deterministic Markov policies.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 15, 2016

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