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Abstract: 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.

The skeleton of this survey are results from Littman, Goldsmith and Mundhenk (Journal of Artificial Intelligence Research 1998), Mundhenk (Mathematics of Operations Research 2000), Mundhenk, Goldsmith, Lusena and Allender (Journal of the ACM 2000), and Lusena, Goldsmith and Mundhenk (University of KY CS TR). But there are also some news.

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   Martin Mundhenk, "The complexity of planning with partially-observable Markov decision processes." Dartmouth Computer Science Technical Report TR2000-376, June 2000.

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