Strong polynomiality of the Gass-Saaty shadow-vertex pivoting rule for controlled random walks

We consider the subclass of linear programs that formulate Markov Decision Processes (mdps). We show that the Simplex algorithm with the Gass-Saaty shadow-vertex pivoting rule is strongly polynomial for a subclass of mdps, called controlled random walks (CRWs); the running time is O({pipe}S{pipe}³{dot operator}{pipe}U{pipe}²), where {pipe}S{pipe} denotes the number of states and {pipe}U{pipe} denotes the number of actions per state. This result improves the running time of Zadorojniy et al. (Mathematics of Operations Research 34(4):992-1007, 2009) algorithm by a factor of {pipe}S{pipe}. In particular, the number of iterations needed by the Simplex algorithm for CRWs is linear in the number of states and does not depend on the discount factor.