  Studies of networked phenomena, such as interactions in online social media,
often rely on incomplete data, either because these phenomena are partially
observed, or because the data is too large or expensive to acquire all at once.
Analysis of incomplete data leads to skewed or misleading results. In this
paper, we investigate limitations of learning to complete partially observed
networks via node querying. Concretely, we study the following problem: given
(i) a partially observed network, (ii) the ability to query nodes for their
connections (e.g., by accessing an API), and (iii) a budget on the number of
such queries, sequentially learn which nodes to query in order to maximally
increase observability. We call this querying process Network Online Learning
and present a family of algorithms called NOL*. These algorithms learn to
choose which partially observed node to query next based on a parameterized
model that is trained online through a process of exploration and exploitation.
Extensive experiments on both synthetic and real world networks show that (i)
it is possible to sequentially learn to choose which nodes are best to query in
a network and (ii) some macroscopic properties of networks, such as the degree
distribution and modular structure, impact the potential for learning and the
optimal amount of random exploration.
