1 research outputs found
Constrained discounted Markov decision processes with Borel state spaces
We study discrete-time discounted constrained Markov decision processes
(CMDPs) on Borel spaces with unbounded reward functions. In our approach the
transition probability functions are weakly or set-wise continuous. The reward
functions are upper semicontinuous in state-action pairs or semicontinuous in
actions. Our aim is to study models with unbounded reward functions, which are
often encountered in applications, e.g., in consumption/investment problems. We
provide some general assumptions under which the optimization problems in CMDPs
are solvable in the class of stationary randomized policies. Then, we indicate
that if the initial distribution and transition probabilities are non-atomic,
then using a general purification result of Feinberg and Piunovskiy, stationary
optimal policies can be deterministic. Our main results are illustrated by five
examples