  Multi-agent active perception is a task where a team of agents cooperatively
gathers observations to compute a joint estimate of a hidden variable. The task
is decentralized and the joint estimate can only be computed after the task
ends by fusing observations of all agents. The objective is to maximize the
accuracy of the estimate. The accuracy is quantified by a centralized
prediction reward determined by a centralized decision-maker who perceives the
observations gathered by all agents after the task ends. In this paper, we
model multi-agent active perception as a decentralized partially observable
Markov decision process (Dec-POMDP) with a convex centralized prediction
reward. We prove that by introducing individual prediction actions for each
agent, the problem is converted into a standard Dec-POMDP with a decentralized
prediction reward. The loss due to decentralization is bounded, and we give a
sufficient condition for when it is zero. Our results allow application of any
Dec-POMDP solution algorithm to multi-agent active perception problems, and
enable planning to reduce uncertainty without explicit computation of joint
estimates. We demonstrate the empirical usefulness of our results by applying a
standard Dec-POMDP algorithm to multi-agent active perception problems, showing
increased scalability in the planning horizon.
