  Metaverse aims for building a fully immersive virtual shared space, where the
users are able to engage in various activities. To successfully deploy the
service for each user, the Metaverse service provider and network service
provider generally localise the user first and then support the communication
between the base station (BS) and the user. A reconfigurable intelligent
surface (RIS) is capable of creating a reflected link between the BS and the
user to enhance line-of-sight. Furthermore, the new key performance indicators
(KPIs) in Metaverse, such as its energy-consumption-dependent total service
cost and transmission latency, are often overlooked in ultra-reliable low
latency communication (URLLC) designs, which have to be carefully considered in
next-generation URLLC (xURLLC) regimes. In this paper, our design objective is
to jointly optimise the transmit power, the RIS phase shifts, and the decoding
error probability to simultaneously minimise the total service cost and
transmission latency and approach the Pareto Front (PF). We conceive a
twin-stage central controller, which aims for localising the users first and
then supports the communication between the BS and users. In the first stage,
we localise the Metaverse users, where the stochastic gradient descent (SGD)
algorithm is invoked for accurate user localisation. In the second stage, a
meta-learning-based position-dependent multi-objective soft actor and critic
(MO-SAC) algorithm is proposed to approach the PF between the total service
cost and transmission latency and to further optimise the latency-dependent
reliability. Our numerical results demonstrate that ...
