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Optimal and Approximate Q-value Functions for Decentralized POMDPs

Frans A. Oliehoek, Matthijs T. J. Spaan, and Nikos Vlassis. Optimal and Approximate Q-value Functions for Decentralized POMDPs. Journal of Artificial Intelligence Research, 32:289–353, 2008.

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Abstract

Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value function Q* is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q*. In this paper we study whether similar Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs), and how policies can be extracted from such value functions. We define two forms of the optimal Q-value function for Dec-POMDPs: one that gives a normative description as the Q-value function of an optimal pure joint policy and another one that is sequentially rational and thus gives a recipe for computation. This computation, however, is infeasible for all but the smallest problems. Therefore, we analyze various approximate Q-value functions that allow for efficient computation. We describe how they relate, and we prove that they all provide an upper bound to the optimal Q-value function Q* . Finally, unifying some previous approaches for solving Dec-POMDPs, we describe a family of algorithms for extracting policies from such Q-value functions, and perform an experimental evaluation on existing test problems, including a new firefighting benchmark problem.

BibTeX Entry

@Article{Oliehoek08JAIR,
  author =       {Frans A. Oliehoek and Matthijs T. J. Spaan and Nikos
                  Vlassis},
  title =        {Optimal and Approximate {Q}-value Functions for
                  Decentralized {POMDPs}},
  journal =      {Journal of Artificial Intelligence Research},
  year =         2008,
  volume =       32,
  pages =        {289--353}
}

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