Abstract
We consider a discounted cost Markov decision process with a constraint. Relating this to a vector-valued Markov decision process, we prove that there exists a constrained optimal randomized semistationary policy if there exists at least one policy satisfying a constraint. Moreover, we present an algorithm by which we can find the constrained optimal randomized semistationary policy, or we can discover that there exist no policies satisfying a given constraint.
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