New value iteration and Q-learning methods for the average cost dynamic programming problem

We propose a new value iteration method for the classical average cost Markovian decision problem, under the assumption that all stationary policies are unichain and furthermore there exists a state that is recurrent under all stationary policies. This method is motivated by a relation between the average cost problem and an associated stochastic shortest path problem. Contrary to the standard relative value iteration, our method involves a weighted sup norm contraction and for this reason it admits a Gauss-Seidel and an asynchronous implementation. Computational tests indicate that the Gauss-Seidel version of the new method substantially outperforms the standard method for difficult problems. The contraction property also makes the method a suitable basis for the development of asynchronous Q-learning methods.