  Hybrid precoding plays a key role in realizing massive multiple-input
multiple-output (MIMO) transmitters with controllable cost. MIMO precoders are
required to frequently adapt based on the variations in the channel conditions.
In hybrid MIMO, here precoding is comprised of digital and analog beamforming,
such an adaptation involves lengthy optimization and depends on accurate
channel state information (CSI). This affects the spectral efficiency when the
channel varies rapidly and when operating with noisy CSI. In this work we
employ deep learning techniques to learn how to rapidly and robustly optimize
hybrid precoders, while being fully interpretable. We leverage data to learn
iteration-dependent hyperparameter settings of projected gradient sum-rate
optimization with a predefined number of iterations. The algorithm maps channel
realizations into hybrid precoding settings while preserving the interpretable
flow of the optimizer and improving its convergence speed. To cope with noisy
CSI, we learn to optimize the minimal achievable sum-rate among all tolerable
errors, proposing a robust hybrid precoding based on the projected conceptual
mirror prox minimax optimizer. Numerical results demonstrate that our approach
allows using over ten times less iterations compared to that required by
conventional optimization with shared hyperparameters, while achieving similar
and even improved sum-rate performance.
