Optimal allocation of resources, such as power and bandwidth, is essential for increasing spectral efficiency and improving effective network capacity to meet the high quality-of-service (QoS) requirements of modern wireless systems. This is especially challenging under randomly varying channel characteristics and user demands. In particular, power allocation in a wireless network is crucial to mitigate multi-user interference, one of the main performance-limiting factors. The task of interference management is framed as a utility maximization problem under instantaneous and/or time-varying power constraints. Such formulations are NP-hard, and the existing solutions are expensive yet sub-optimal at best. Recently, deep learning algorithms have been extensively employed to obtain approximate solvers efficiently. In particular, graph-based models have been shown to be most effective in leveraging the irregular connectivity structure of wireless networks.

In this thesis, we focus on developing near-optimal, generalizable, lightweight, and robust Graph Neural Network (GNN)-based algorithms for effectively solving NP-hard optimization problems in wireless systems under instantaneous and time-varying constraints. The first part of this work specializes in designing domain-informed graph-ML algorithms by leveraging the paradigm of algorithm unfolding for fast and efficient instantaneous power allocation in SISO wireless ad hoc networks (WANET) with theoretically guaranteed convergence and robustness. The next part involves extending the unfolded solution and the theoretical analyses to address the optimal beamforming problem in MISO and MIMO interference networks under max-power constraints. The final part leverages constrained reinforcement learning algorithms for episodic sum-rate and harmonic-fairness maximization under time-varying battery constraints and channel conditions in mobile WANETs (MANET). Through these bodies of work, this thesis develops a unified framework for power allocation under time-coupled physical and utility constraints in wireless networks.

Through \blue{simulation experiments}, we demonstrate a consistent performance improvement over SOTA models, both in terms of system utility and inference time. We also establish the generalization performance of the proposed models across multiple network topologies, sizes, fading conditions, and battery states. Further, we show that the proposed architectures are computationally efficient and can be executed with minimal hardware requirements. The hybrid structure of the models enhances interpretability as well as acts as a fail-safe in case the learnable components are no longer effective. Finally, the proposed framework is flexible and can be seamlessly applied to multiple tasks, including resource allocation, security, and control in wireless networks and systems.