9,026 research outputs found
Asynchronous Gossip for Averaging and Spectral Ranking
We consider two variants of the classical gossip algorithm. The first variant
is a version of asynchronous stochastic approximation. We highlight a
fundamental difficulty associated with the classical asynchronous gossip
scheme, viz., that it may not converge to a desired average, and suggest an
alternative scheme based on reinforcement learning that has guaranteed
convergence to the desired average. We then discuss a potential application to
a wireless network setting with simultaneous link activation constraints. The
second variant is a gossip algorithm for distributed computation of the
Perron-Frobenius eigenvector of a nonnegative matrix. While the first variant
draws upon a reinforcement learning algorithm for an average cost controlled
Markov decision problem, the second variant draws upon a reinforcement learning
algorithm for risk-sensitive control. We then discuss potential applications of
the second variant to ranking schemes, reputation networks, and principal
component analysis.Comment: 14 pages, 7 figures. Minor revisio
Novel Multidimensional Models of Opinion Dynamics in Social Networks
Unlike many complex networks studied in the literature, social networks
rarely exhibit unanimous behavior, or consensus. This requires a development of
mathematical models that are sufficiently simple to be examined and capture, at
the same time, the complex behavior of real social groups, where opinions and
actions related to them may form clusters of different size. One such model,
proposed by Friedkin and Johnsen, extends the idea of conventional consensus
algorithm (also referred to as the iterative opinion pooling) to take into
account the actors' prejudices, caused by some exogenous factors and leading to
disagreement in the final opinions.
In this paper, we offer a novel multidimensional extension, describing the
evolution of the agents' opinions on several topics. Unlike the existing
models, these topics are interdependent, and hence the opinions being formed on
these topics are also mutually dependent. We rigorous examine stability
properties of the proposed model, in particular, convergence of the agents'
opinions. Although our model assumes synchronous communication among the
agents, we show that the same final opinions may be reached "on average" via
asynchronous gossip-based protocols.Comment: Accepted by IEEE Transaction on Automatic Control (to be published in
May 2017
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