In this paper, the aim is to study the robustness against imperfect channel state information (CSI) of the power allocation policies maximizing the constrained and non-convex Shannon rate problem in a relay-aided cognitive radio network. The primary communication is protected by a Quality of Service (QoS) constraint and the relay only helps the secondary communication by performing complex and non-linear operations. First, we derive the optimal power allocation policies under Compress-and-Forward (CF) relaying under perfect CSI. Second, we investigate the robustness of this solution jointly with that of the deep learning existing solution for Decode-and-Forward (DF), which we exploit here for CF as well. For all these solutions that strongly rely on perfect CSI, our numerical results show that errors in the channel estimations have a damaging effect not only on the secondary rate, but most importantly on the primary QoS degradation, becoming prohibitive for poor quality estimations. Nevertheless, we show that the deep learning solutions can be made robust by adjusting the training process to rely on both perfect and imperfect CSI observations. Indeed, the resulting predictions are capable of meeting the primary QoS constraint at the cost of secondary rate loss, irrespective from the channel estimation quality.