2 research outputs found
The domination number of on-line social networks and random geometric graphs
We consider the domination number for on-line social networks, both in a
stochastic network model, and for real-world, networked data. Asymptotic
sublinear bounds are rigorously derived for the domination number of graphs
generated by the memoryless geometric protean random graph model. We establish
sublinear bounds for the domination number of graphs in the Facebook 100 data
set, and these bounds are well-correlated with those predicted by the
stochastic model. In addition, we derive the asymptotic value of the domination
number in classical random geometric graphs
Collaborative Learning of Stochastic Bandits over a Social Network
We consider a collaborative online learning paradigm, wherein a group of
agents connected through a social network are engaged in playing a stochastic
multi-armed bandit game. Each time an agent takes an action, the corresponding
reward is instantaneously observed by the agent, as well as its neighbours in
the social network. We perform a regret analysis of various policies in this
collaborative learning setting. A key finding of this paper is that natural
extensions of widely-studied single agent learning policies to the network
setting need not perform well in terms of regret. In particular, we identify a
class of non-altruistic and individually consistent policies, and argue by
deriving regret lower bounds that they are liable to suffer a large regret in
the networked setting. We also show that the learning performance can be
substantially improved if the agents exploit the structure of the network, and
develop a simple learning algorithm based on dominating sets of the network.
Specifically, we first consider a star network, which is a common motif in
hierarchical social networks, and show analytically that the hub agent can be
used as an information sink to expedite learning and improve the overall
regret. We also derive networkwide regret bounds for the algorithm applied to
general networks. We conduct numerical experiments on a variety of networks to
corroborate our analytical results.Comment: 14 Pages, 6 Figure