Edge networks pose unique challenges for machine learning and network management. The primary objective of this dissertation is to study deep learning and adaptive control aspects of edge networks and to address some of the unique challenges therein. This dissertation explores four particular problems of interest at the intersection of edge intelligence, deep learning and network management. The first problem explores the learning of generative models in edge learning setting. Since the learning tasks in similar environments share model similarity, it is plausible to leverage pre-trained generative models from other edge nodes. Appealing to optimal transport theory tailored towards Wasserstein-1 generative adversarial networks, this part aims to develop a framework which systematically optimizes the generative model learning performance using local data at the edge node while exploiting the adaptive coalescence of pre-trained generative models from other nodes. In the second part, a many-to-one wireless architecture for federated learning at the network edge, where multiple edge devices collaboratively train a model using local data, is considered. The unreliable nature of wireless connectivity, togetherwith the constraints in computing resources at edge devices, dictates that the local updates at edge devices should be carefully crafted and compressed to match the wireless communication resources available and should work in concert with the receiver. Therefore, a Stochastic Gradient Descent based bandlimited coordinate descent algorithm is designed for such settings. The third part explores the adaptive traffic engineering algorithms in a dynamic network environment. The ages of traffic measurements exhibit significant variation due to asynchronization and random communication delays between routers and controllers. Inspired by the software defined networking architecture, a controller-assisted distributed routing scheme with recursive link weight reconfigurations, accounting for the impact of measurement ages and routing instability, is devised. The final part focuses on developing a federated learning based framework for traffic reshaping of electric vehicle (EV) charging. The absence of private EV owner information and scattered EV charging data among charging stations motivates the utilization of a federated learning approach. Federated learning algorithms are devised to minimize peak EV charging demand both spatially and temporarily, while maximizing the charging station profit.