  Multi-access edge computing (MEC) is a promising solution to the
computation-intensive, low-latency rendering tasks of the metaverse. However,
how to optimally allocate limited communication and computation resources at
the edge to a large number of users in the metaverse is quite challenging. In
this paper, we propose an adaptive edge resource allocation method based on
multi-agent soft actor-critic with graph convolutional networks (SAC-GCN).
Specifically, SAC-GCN models the multi-user metaverse environment as a graph
where each agent is denoted by a node. Each agent learns the interplay between
agents by graph convolutional networks with self-attention mechanism to further
determine the resource usage for one user in the metaverse. The effectiveness
of SAC-GCN is demonstrated through the analysis of user experience, balance of
resource allocation, and resource utilization rate by taking a virtual city
park metaverse as an example. Experimental results indicate that SAC-GCN
outperforms other resource allocation methods in improving overall user
experience, balancing resource allocation, and increasing resource utilization
rate by at least 27%, 11%, and 8%, respectively.
