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In this paper, a deep learning (DL) framework for the optimization of the resource allocation in multi-channel cellular systems with device-to-device (D2D) communication is proposed. Thereby, the channel assignment and discrete transmit power levels of the D2D users, which are both integer variables, are optimized to maximize the overall spectral efficiency whilst maintaining the quality-of-service (QoS) of the cellular users. Depending on the availability of channel state information (CSI), two different configurations are considered, namely 1) centralized operation with full CSI and 2) distributed operation with partial CSI, where in the latter case, the CSI is encoded according to the capacity of the feedback channel. Instead of solving the resulting resource allocation problem for each channel realization, a DL framework is proposed, where the optimal resource allocation strategy for arbitrary channel conditions is approximated by deep neural network (DNN) models. Furthermore, we propose a new training strategy that combines supervised and unsupervised learning methods and a local CSI sharing strategy to achieve near-optimal performance while enforcing the QoS constraints of the cellular users and efficiently handling the integer optimization variables based on a few ground-truth labels. Our simulation results confirm that near-optimal performance can be attained with low computation time, which underlines the real-time capability of the proposed scheme. Moreover, our results show that not only the resource allocation strategy but also the CSI encoding strategy can be efficiently determined using a DNN. Furthermore, we show that the proposed DL framework can be easily extended to communications systems with different design objectives.