Internet of Things (IoT) technologies have made considerable recent advances in commercial applications, prompting new research on their use in military applications. Towards the development of an Internet of Battlefield Things (IoBT), capable of leveraging mixed commercial and military technologies, several unique challenges of the tactical environment present themselves. These challenges include development of methods for: (I) quickly gathering training data reflecting unforeseen learning/classification tasks; (II) incrementally learning over real-time data streams; (III) management of limited network bandwidth and connectivity between IoBT assets in data gathering and classification tasks. This paper provides a survey over classical and modern statistical learning theory, and how numerical optimization can be used to solve corresponding mathematical problems. The objective of this paper is to encourage the IoT and machine learning research communities to revisit the underlying mathematical underpinnings of stream-based learning, as applicable to IoBT-based systems.