The Complexity of Decentralized Control of Markov Decision Processes
Daniel Bernstein, Shlomo Zilberstein, Neil Immerman
Planning for distributed agents with partial state information is considered from a decision- theoretic perspective. We describe generalizations of both the MDP and POMDP models that allow for decentralized control. For even a small number of agents, the finite-horizon problems corresponding to both of our models are complete for nondeterministic exponential time. These complexity results illustrate a fundamental difference between centralized and decentralized control of Markov processes. In contrast to the MDP and POMDP problems, the problems we consider provably do not admit polynomial-time algorithms and most likely require doubly exponential time to solve in the worst case. We have thus provided mathematical evidence corresponding to the intuition that decentralized planning problems cannot easily be reduced to centralized problems and solved exactly using established techniques.
Keywords: Markov decision processes, computational complexity, decentralized control
PS Link: http://www-anw.cs.umass.edu/~bern/Publications/Uai00.ps
PDF Link: /papers/00/p32-bernstein.pdf
AUTHOR = "Daniel Bernstein
and Shlomo Zilberstein and Neil Immerman",
TITLE = "The Complexity of Decentralized Control of Markov Decision Processes",
BOOKTITLE = "Proceedings of the Sixteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-00)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "2000",
PAGES = "32--37"