Approximation of average cost optimal policies for general Markov decision processes with unbounded costs

The aim of the paper is to show that Lyapunov-like ergodicity conditions on Markov decision processes with Borel state space and possibly unbounded cost provide the approximation of an average cost optimal policy by solving n-stage optimization problems (n = 1, 2, …). The used approach ensures the exponential rate of convergence. The approximation of this type would be useful to find adaptive procedures of control and to estimate stability of an optimal control under disturbances of the transition probability.