  Decision-making problems in uncertain or stochastic domains are often
formulated as Markov decision processes (MDPs). Policy iteration (PI) is a
popular algorithm for searching over policy-space, the size of which is
exponential in the number of states. We are interested in bounds on the
complexity of PI that do not depend on the value of the discount factor. In
this paper we prove the first such non-trivial, worst-case, upper bounds on the
number of iterations required by PI to converge to the optimal policy. Our
analysis also sheds new light on the manner in which PI progresses through the
space of policies.
