In this paper, an unsupervised deep learning approach is proposed to solve the constrained and non-convex Shannon rate maximization problem in a relay-aided cognitive radio network. This network consists of a primary and a secondary user-destination pair and a secondary full-duplex relay performing Decode-and-Forward. The primary communication is protected by a Quality of Service (QoS) constraint in terms of tolerated Shannon rate degradation. The relaying operation leads to non-convex objective and primary QoS constraint, which makes deep learning approaches relevant and promising. For this, we propose a fully-connected neural network architecture coupled with a custom and communication-tailored loss function to be minimized during training in an unsupervised manner. A major interest of our approach is that the required training data contains only system parameters without the corresponding solutions to the non-convex optimization problem, as opposed to supervised approaches. Our numerical experiments show that our proposed approach has a high generalization capability on unseen data without overfitting. Also, the predicted solution performs close to the brute force one, highlighting the high potential of our unsupervised approach.