With the proliferation of smart devices, it is increasingly important to exploit their computing, networking, and storage resources for executing various computing tasks at scale at mobile network edges, bringing many benefits such as better response time, network bandwidth savings, and improved data privacy and security. A key component in enabling such distributed edge computing is a mechanism that can flexibly and dynamically manage edge resources for running various military and commercial applications in a manner adaptive to the fluctuating demands and resource availability. We present methods and an architecture for the edge resource management based on machine learning techniques. A collaborative filtering approach combined with deep learning is proposed as a means to build the predictive model for applications' performance on resources from previous observations, and an online resource allocation architecture utilizing the predictive model is presented. We also identify relevant research topics for further investigation.