  Reconfigurable Intelligent Surfaces (RISs) are regarded as a key technology
for future wireless communications, enabling programmable radio propagation
environments. However, the passive reflecting feature of RISs induces notable
challenges on channel estimation, making coherent symbol detection a
challenging task. In this paper, we consider the uplink of RIS-aided multi-user
Multiple-Input Multiple-Output (MIMO) systems and propose a Machine Learning
(ML) approach to jointly design the multi-antenna receiver and configure the
RIS reflection coefficients, which does not require explicit full knowledge of
the channel input-output relationship. Our approach devises a ML-based
receiver, while the configurations of the RIS reflection patterns affecting the
underlying propagation channel are treated as hyperparameters. Based on this
system design formulation, we propose a Bayesian ML framework for optimizing
the RIS hyperparameters, according to which the transmitted pilots are directly
used to jointly tune the RIS and the multi-antenna receiver. Our simulation
results demonstrate the capability of the proposed approach to provide reliable
communications in non-linear channel conditions corrupted by Gaussian noise.
