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.