  This article presents the state-of-the-art in optimal solution methods for
decentralized partially observable Markov decision processes (Dec-POMDPs),
which are general models for collaborative multiagent planning under
uncertainty. Building off the generalized multiagent A* (GMAA*) algorithm,
which reduces the problem to a tree of one-shot collaborative Bayesian games
(CBGs), we describe several advances that greatly expand the range of
Dec-POMDPs that can be solved optimally. First, we introduce lossless
incremental clustering of the CBGs solved by GMAA*, which achieves exponential
speedups without sacrificing optimality. Second, we introduce incremental
expansion of nodes in the GMAA* search tree, which avoids the need to expand
all children, the number of which is in the worst case doubly exponential in
the nodes depth. This is particularly beneficial when little clustering is
possible. In addition, we introduce new hybrid heuristic representations that
are more compact and thereby enable the solution of larger Dec-POMDPs. We
provide theoretical guarantees that, when a suitable heuristic is used, both
incremental clustering and incremental expansion yield algorithms that are both
complete and search equivalent. Finally, we present extensive empirical results
demonstrating that GMAA*-ICE, an algorithm that synthesizes these advances, can
optimally solve Dec-POMDPs of unprecedented size.
