Q-value functions for decentralized POMDPs

Planning in single-agent models like MDPs and POMDPs can be carried out by resorting to Q-value functions: a (near-) optimal Q-value function is computed in a recursive manner by dynamic programming, and then a policy is extracted from this value function. In this paper we study whether similar Q-value functions can be defined in decentralized POMDP models (Dec-POMDPs), what the cost of computing such value functions is, and how policies can be extracted from such value functions. Using the framework of Bayesian games, we argue that searching for the optimal Q-value function may be as costly as exhaustive policy search. Then we analyze various approximate Q-value functions that allow efficient computation. Finally, we describe a family of algorithms for extracting policies from such Q-value functions.