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Influence Maximization with Bandits
We consider the problem of \emph{influence maximization}, the problem of
maximizing the number of people that become aware of a product by finding the
`best' set of `seed' users to expose the product to. Most prior work on this
topic assumes that we know the probability of each user influencing each other
user, or we have data that lets us estimate these influences. However, this
information is typically not initially available or is difficult to obtain. To
avoid this assumption, we adopt a combinatorial multi-armed bandit paradigm
that estimates the influence probabilities as we sequentially try different
seed sets. We establish bounds on the performance of this procedure under the
existing edge-level feedback as well as a novel and more realistic node-level
feedback. Beyond our theoretical results, we describe a practical
implementation and experimentally demonstrate its efficiency and effectiveness
on four real datasets.Comment: 12 page
Stability of Influence Maximization
The present article serves as an erratum to our paper of the same title,
which was presented and published in the KDD 2014 conference. In that article,
we claimed falsely that the objective function defined in Section 1.4 is
non-monotone submodular. We are deeply indebted to Debmalya Mandal, Jean
Pouget-Abadie and Yaron Singer for bringing to our attention a counter-example
to that claim.
Subsequent to becoming aware of the counter-example, we have shown that the
objective function is in fact NP-hard to approximate to within a factor of
for any .
In an attempt to fix the record, the present article combines the problem
motivation, models, and experimental results sections from the original
incorrect article with the new hardness result. We would like readers to only
cite and use this version (which will remain an unpublished note) instead of
the incorrect conference version.Comment: Erratum of Paper "Stability of Influence Maximization" which was
presented and published in the KDD1
Online Influence Maximization (Extended Version)
Social networks are commonly used for marketing purposes. For example, free
samples of a product can be given to a few influential social network users (or
"seed nodes"), with the hope that they will convince their friends to buy it.
One way to formalize marketers' objective is through influence maximization (or
IM), whose goal is to find the best seed nodes to activate under a fixed
budget, so that the number of people who get influenced in the end is
maximized. Recent solutions to IM rely on the influence probability that a user
influences another one. However, this probability information may be
unavailable or incomplete. In this paper, we study IM in the absence of
complete information on influence probability. We call this problem Online
Influence Maximization (OIM) since we learn influence probabilities at the same
time we run influence campaigns. To solve OIM, we propose a multiple-trial
approach, where (1) some seed nodes are selected based on existing influence
information; (2) an influence campaign is started with these seed nodes; and
(3) users' feedback is used to update influence information. We adopt the
Explore-Exploit strategy, which can select seed nodes using either the current
influence probability estimation (exploit), or the confidence bound on the
estimation (explore). Any existing IM algorithm can be used in this framework.
We also develop an incremental algorithm that can significantly reduce the
overhead of handling users' feedback information. Our experiments show that our
solution is more effective than traditional IM methods on the partial
information.Comment: 13 pages. To appear in KDD 2015. Extended versio
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