The Complexity of Decentralized Control of Markov Decision Processes

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The Complexity of Decentralized Control of Markov Decision Processes (2000)

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by Daniel S. Bernstein , Robert Givan , Neil Immerman , Shlomo Zilberstein

Venue:	Mathematics of Operations Research
Citations:	411 - 46 self

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@INPROCEEDINGS{Bernstein00thecomplexity,
    author = {Daniel S. Bernstein and Robert Givan and Neil Immerman and Shlomo Zilberstein},
    title = {The Complexity of Decentralized Control of Markov Decision Processes},
    booktitle = {Mathematics of Operations Research},
    year = {2000},
    pages = {2002}
}

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Abstract

We consider decentralized control of Markov decision processes and give complexity bounds on the worst-case running time for algorithms that find optimal solutions. Generalizations of both the fullyobservable case and the partially-observable case that allow for decentralized control are described. For even two agents, the finite-horizon problems corresponding to both of these models are hard for nondeterministic exponential time. These complexity results illustrate a fundamental difference between centralized and decentralized control of Markov decision processes. In contrast to the problems involving centralized control, the problems we consider provably do not admit polynomial-time algorithms. Furthermore, assuming EXP NEXP, the problems require super-exponential time to solve in the worst case.

Keyphrases

markov decision process decentralized control fundamental difference finite-horizon problem optimal solution markov decision partially-observable case polynomial-time algorithm super-exponential time complexity bound nondeterministic exponential time worst-case running time complexity result exp nexp fullyobservable case

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