Mundhenk:
The Complexity of Planning with Partially Observable Markov Decision Processes

This work surveys results on the complexity of planning under uncertainty. The planning model considered is the partially-observable Markov decision process. The general planning problems are, given such a process, (a) to calculate its performance under a given control policy, (b) to find an optimal or approximate optimal control policy, and (c) to decide whether a good policy exists. The complexity of this and related problems depend on a variety of factors, including the observability of the process state, the compactness of the process representation, the type of policy, or even the number of actions relative to the number of states. In most cases, the problem can be shown to be complete for some known complexity class.