  This paper investigates a learning solution for robust beamforming
optimization in downlink multi-user systems. A base station (BS) identifies
efficient multi-antenna transmission strategies only with imperfect channel
state information (CSI) and its stochastic features. To this end, we propose a
robust training algorithm where a deep neural network (DNN), which only accepts
estimates and statistical knowledge of the perfect CSI, is optimized to fit to
real-world propagation environment. Consequently, the trained DNN can provide
efficient robust beamforming solutions based only on imperfect observations of
the actual CSI. Numerical results validate the advantages of the proposed
learning approach compared to conventional schemes.
