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.