No abstract

Constrained Markov decision processes with compact state and action spaces are studied under long-run average reward or cost criteria. And introducing a corresponding Lagrange function, a saddle-point theorem is given, by which the existence of a constrained optimal pair of initial state distribution and policy is shown. Also, under the hypothesis of Doeblin, the functional characterization of a constrained optimal policy is obtained.

In the framework of discounted Markov decision processes, we consider the case that the transition probability varies in some given domain at each time and its variation is unknown or unobservable.To this end we introduce a new model, named controlled Markov set-chains, based on Markov set-chains, and discuss its optimization under some partial order.Also, a numerical example is given to explain the theoretical results and the computation.

No abstract

In the framework of discounted Markov decision processes, we consider the case that the transition probability varies in some given domain at each time and its variation is unknown or unobservable. To this end we introduce a new model, named controlled Markov set-chains, based on Markov set-chains, and discuss its optimization under some partial order. Also, a numerical example is given to explain the theoretical results and the computation.