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.

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