Wireless network optimization faces challenges in several aspects. System-level objective functions are typically non-convex due to multiuser interference, rendering NP-hard problems. Moreover, real-world factors like delay and energy requirements could translate into non-convex constraints. As a result, traditional practices tend to be suboptimal and often rely on computationally expensive iterations or simulations. This inefficiency limits the design and management of scalable wireless networks.

To improve efficiency, this thesis leverages deep learning techniques, with a focus on the permutation-equivariant graph neural networks (GNNs), across various wireless applications. The first part of this thesis presents a graph-based trainable framework for power allocation, namely the unfolded successive concave approximation (USCA), to maximize weighted-sum energy efficiency (WSEE) in wireless interference networks. The second part revisits power allocation and, by devising a primal-dual (PD) learning framework, handles non-convex constraints specific to the context of wireless federated learning (FL). Finally, the third part creates a learnable digital twin (DT) for efficient network evaluation, a thousandfold more efficient tool than simulators for network design and management. These three bodies of work demonstrate comprehensive theoretical and experimental results highlighting the superior performance of the proposed architectures over existing approaches.

Overall, this work seeks to integrate deep learning into wireless applications by innovating specialized architectures that retain the core structure of original regimes. Key advantages include better interpretability than non-specialized end-to-end learning, enhanced generalizability across varying network configurations, and faster inference speed compared to optimization-based methods and simulators. The methodologies presented herein have substantial potential for diverse wireless applications, including network design, resource allocation, and network management.