Encyclopaedia of Complexity Results for Finite-horizon Markov Decision Process Problems 1

The computational complexity of nite horizon policy evaluation and policy existence problems are studied for several policy types and representations of Markov decision processes. In almost all cases, the problems are shown to be complete for their complexity classes; classes range from nondeterministic logarithmic space and probabilistic logarithmic space (highly parallelizable classes) to exponential space. In many cases, this work shows that problems that already were widely believed to be hard to compute are probably intractable (complete for NP, NPPP, or PSPACE), or provably intractable (EXPTIME-complete or worse). The major contributions of the paper are to pinpoint the complexity of these problems; to isolate the factors that make these problems computationally complex; to show that even problems such as median-policy or average-policy evaluation may be intractable; and the introduction of natural NPPP-complete problems.