  The gang of bandits (GOB) model \cite{cesa2013gang} is a recent contextual
bandits framework that shares information between a set of bandit problems,
related by a known (possibly noisy) graph. This model is useful in problems
like recommender systems where the large number of users makes it vital to
transfer information between users. Despite its effectiveness, the existing GOB
model can only be applied to small problems due to its quadratic
time-dependence on the number of nodes. Existing solutions to combat the
scalability issue require an often-unrealistic clustering assumption. By
exploiting a connection to Gaussian Markov random fields (GMRFs), we show that
the GOB model can be made to scale to much larger graphs without additional
assumptions. In addition, we propose a Thompson sampling algorithm which uses
the recent GMRF sampling-by-perturbation technique, allowing it to scale to
even larger problems (leading to a "horde" of bandits). We give regret bounds
and experimental results for GOB with Thompson sampling and epoch-greedy
algorithms, indicating that these methods are as good as or significantly
better than ignoring the graph or adopting a clustering-based approach.
Finally, when an existing graph is not available, we propose a heuristic for
learning it on the fly and show promising results.
