  Real-world networks such as social and communication networks are too large
to be observed entirely. Such networks are often partially observed such that
network size, network topology, and nodes of the original network are unknown.
In this paper we formalize the Adaptive Graph Exploring problem. We assume that
we are given an incomplete snapshot of a large network and additional nodes can
be discovered by querying nodes in the currently observed network. The goal of
this problem is to maximize the number of observed nodes within a given query
budget. Querying which set of nodes maximizes the size of the observed network?
We formulate this problem as an exploration-exploitation problem and propose a
novel nonparametric multi-arm bandit (MAB) algorithm for identifying which
nodes to be queried. Our contributions include: (1) $i$KNN-UCB, a novel
nonparametric MAB algorithm, applies $k$-nearest neighbor UCB to the setting
when the arms are presented in a vector space, (2) provide theoretical
guarantee that $i$KNN-UCB algorithm has sublinear regret, and (3) applying
$i$KNN-UCB algorithm on synthetic networks and real-world networks from
different domains, we show that our method discovers up to 40% more nodes
compared to existing baselines.
