The Complexity of Optimal Small Policies

Authors:
Martin Mundhenk
Affiliations:
-
Venue:
Mathematics of Operations Research
Year:
2000

Citing 0
Cited 2

Complexity of finite-horizon Markov decision process problems

Journal of the ACM (JACM)
Nonapproximability results for partially observable Markov decision processes

Journal of Artificial Intelligence Research

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Abstract

We investigate the complexity of problems concerned with partially-observable Markov decision processes which are run for a finite number of steps under small policies. The calculation of the expected sum of rewards of a process under a small policy is shown to be complete for the complexity class PP, a class which lies intermediate between NP and PSPACE. Optimal small policy computation is shown to be complete for NP PP. The latter contrasts results of Papadimitriou and Tsitsiklis (Papadimitriou and Tsitsiklis 1987), who showed that this problem is PSPACE-complete, if no assumptions about the representability of the policy are made, and that it is P-complete for fully-observable processes.