  We introduce a novel deep reinforcement learning (DRL) approach to jointly
optimize transmit beamforming and reconfigurable intelligent surface (RIS)
phase shifts in a multiuser multiple input single output (MU-MISO) system to
maximize the sum downlink rate under the phase-dependent reflection amplitude
model. Our approach addresses the challenge of imperfect channel state
information (CSI) and hardware impairments by considering a practical RIS
amplitude model. We compare the performance of our approach against a vanilla
DRL agent in two scenarios: perfect CSI and phase-dependent RIS amplitudes, and
mismatched CSI and ideal RIS reflections. The results demonstrate that the
proposed framework significantly outperforms the vanilla DRL agent under
mismatch and approaches the golden standard. Our contributions include
modifications to the DRL approach to address the joint design of transmit
beamforming and phase shifts and the phase-dependent amplitude model. To the
best of our knowledge, our method is the first DRL-based approach for the
phase-dependent reflection amplitude model in RIS-aided MU-MISO systems. Our
findings in this study highlight the potential of our approach as a promising
solution to overcome hardware impairments in RIS-aided wireless communication
systems.
