  Deep neural networks (DNN) can approximate value functions or policies for
reinforcement learning, which makes the reinforcement learning algorithms more
powerful. However, some DNNs, such as convolutional neural networks (CNN),
cannot extract enough information or take too long to obtain enough features
from the inputs under specific circumstances of reinforcement learning. For
example, the input data of Google Research Football, a reinforcement learning
environment which trains agents to play football, is the small map of players'
locations. The information is contained not only in the coordinates of players,
but also in the relationships between different players. CNNs can neither
extract enough information nor take too long to train. To address this issue,
this paper proposes a deep q-learning network (DQN) with a graph neural network
(GNN) as its model. The GNN transforms the input data into a graph which better
represents the football players' locations so that it extracts more information
of the interactions between different players. With two GNNs to approximate its
local and target value functions, this DQN allows players to learn from their
experience by using value functions to see the prospective value of each
intended action. The proposed model demonstrated the power of GNN in the
football game by outperforming other DRL models with significantly fewer steps.
