  The gameplay of strategic board games such as chess, Go and Hex is often
characterized by combinatorial, relational structures -- capturing distinct
interactions and non-local patterns -- and not just images. Nonetheless, most
common self-play reinforcement learning (RL) approaches simply approximate
policy and value functions using convolutional neural networks (CNN). A key
feature of CNNs is their relational inductive bias towards locality and
translational invariance. In contrast, graph neural networks (GNN) can encode
more complicated and distinct relational structures. Hence, we investigate the
crucial question: Can GNNs, with their ability to encode complex connections,
replace CNNs in self-play reinforcement learning? To this end, we do a
comparison with Hex -- an abstract yet strategically rich board game -- serving
as our experimental platform. Our findings reveal that GNNs excel at dealing
with long range dependency situations in game states and are less prone to
overfitting, but also showing a reduced proficiency in discerning local
patterns. This suggests a potential paradigm shift, signaling the use of
game-specific structures to reshape self-play reinforcement learning.
