  In multi-agent reinforcement learning, the use of a global objective is a
powerful tool for incentivising cooperation. Unfortunately, it is not
sample-efficient to train individual agents with a global reward, because it
does not necessarily correlate with an agent's individual actions. This problem
can be solved by factorising the global value function into local value
functions. Early work in this domain performed factorisation by conditioning
local value functions purely on local information. Recently, it has been shown
that providing both local information and an encoding of the global state can
promote cooperative behaviour. In this paper we propose QGNN, the first value
factorisation method to use a graph neural network (GNN) based model. The
multi-layer message passing architecture of QGNN provides more representational
complexity than models in prior work, allowing it to produce a more effective
factorisation. QGNN also introduces a permutation invariant mixer which is able
to match the performance of other methods, even with significantly fewer
parameters. We evaluate our method against several baselines, including
QMIX-Att, GraphMIX, QMIX, VDN, and hybrid architectures. Our experiments
include Starcraft, the standard benchmark for credit assignment; Estimate Game,
a custom environment that explicitly models inter-agent dependencies; and
Coalition Structure Generation, a foundational problem with real-world
applications. The results show that QGNN outperforms state-of-the-art value
factorisation baselines consistently.
