## Publications• Sorted by Date • Classified by Publication Type • Classified by Research Category • ## 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. ## Downloadpdf [613.0kB] ps.gz [403.8kB] ps HTML ## AbstractDecision-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 = JAIR, year = 2008, volume = {32}, pages = {289--353}, url = {https://doi.org/10.1613/jair.2447}, doi = {10.1613/jair.2447}, 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. } } Generated by bib2html.pl (written by Patrick Riley) on Mon May 22, 2023 14:38:02 UTC |