  Reconfigurable intelligent surface (RIS) is capable of intelligently
manipulating the phases of the incident electromagnetic wave to improve the
wireless propagation environment between the base-station (BS) and the users.
This paper addresses the joint user scheduling, RIS configuration, and BS
beamforming problem in an RIS-assisted downlink network with limited pilot
overhead. We show that graph neural networks (GNN) with permutation invariant
and equivariant properties can be used to appropriately schedule users and to
design RIS configurations to achieve high overall throughput while accounting
for fairness among the users. As compared to the conventional methodology of
first estimating the channels then optimizing the user schedule, RIS
configuration and the beamformers, this paper shows that an optimized user
schedule can be obtained directly from a very short set of pilots using a GNN,
then the RIS configuration can be optimized using a second GNN, and finally the
BS beamformers can be designed based on the overall effective channel.
Numerical results show that the proposed approach can utilize the received
pilots more efficiently than the conventional channel estimation based
approach, and can generalize to systems with an arbitrary number of users.
