  Centralized training with decentralized execution has become an important
paradigm in multi-agent learning. Though practical, current methods rely on
restrictive assumptions to decompose the centralized value function across
agents for execution. In this paper, we eliminate this restriction by proposing
multi-agent determinantal Q-learning. Our method is established on Q-DPP, an
extension of determinantal point process (DPP) with partition-matroid
constraint to multi-agent setting. Q-DPP promotes agents to acquire diverse
behavioral models; this allows a natural factorization of the joint Q-functions
with no need for \emph{a priori} structural constraints on the value function
or special network architectures. We demonstrate that Q-DPP generalizes major
solutions including VDN, QMIX, and QTRAN on decentralizable cooperative tasks.
To efficiently draw samples from Q-DPP, we adopt an existing
sample-by-projection sampler with theoretical approximation guarantee. The
sampler also benefits exploration by coordinating agents to cover orthogonal
directions in the state space during multi-agent training. We evaluate our
algorithm on various cooperative benchmarks; its effectiveness has been
demonstrated when compared with the state-of-the-art.
