88 research outputs found
On Distributed Averaging Algorithms and Quantization Effects
We consider distributed iterative algorithms for the averaging problem over
time-varying topologies. Our focus is on the convergence time of such
algorithms when complete (unquantized) information is available, and on the
degradation of performance when only quantized information is available. We
study a large and natural class of averaging algorithms, which includes the
vast majority of algorithms proposed to date, and provide tight polynomial
bounds on their convergence time. We also describe an algorithm within this
class whose convergence time is the best among currently available averaging
algorithms for time-varying topologies. We then propose and analyze distributed
averaging algorithms under the additional constraint that agents can only store
and communicate quantized information, so that they can only converge to the
average of the initial values of the agents within some error. We establish
bounds on the error and tight bounds on the convergence time, as a function of
the number of quantization levels
On Convergence Rate of Scalar Hegselmann-Krause Dynamics
In this work, we derive a new upper bound on the termination time of the
Hegselmann-Krause model for opinion dynamics. Using a novel method, we show
that the termination rate of this dynamics happens no longer than
which improves the best known upper bound of by a factor of .Comment: 5 pages, 2 figures, submitted to The American Control Conference,
Sep. 201
An Upper Bound on the Convergence Time for Quantized Consensus of Arbitrary Static Graphs
We analyze a class of distributed quantized consensus algorithms for
arbitrary static networks. In the initial setting, each node in the network has
an integer value. Nodes exchange their current estimate of the mean value in
the network, and then update their estimation by communicating with their
neighbors in a limited capacity channel in an asynchronous clock setting.
Eventually, all nodes reach consensus with quantized precision. We analyze the
expected convergence time for the general quantized consensus algorithm
proposed by Kashyap et al \cite{Kashyap}. We use the theory of electric
networks, random walks, and couplings of Markov chains to derive an upper bound for the expected convergence time on an arbitrary graph of size
, improving on the state of art bound of for quantized consensus
algorithms. Our result is not dependent on graph topology. Example of complete
graphs is given to show how to extend the analysis to graphs of given topology.Comment: to appear in IEEE Trans. on Automatic Control, January, 2015. arXiv
admin note: substantial text overlap with arXiv:1208.078
Exponentially Fast Parameter Estimation in Networks Using Distributed Dual Averaging
In this paper we present an optimization-based view of distributed parameter
estimation and observational social learning in networks. Agents receive a
sequence of random, independent and identically distributed (i.i.d.) signals,
each of which individually may not be informative about the underlying true
state, but the signals together are globally informative enough to make the
true state identifiable. Using an optimization-based characterization of
Bayesian learning as proximal stochastic gradient descent (with
Kullback-Leibler divergence from a prior as a proximal function), we show how
to efficiently use a distributed, online variant of Nesterov's dual averaging
method to solve the estimation with purely local information. When the true
state is globally identifiable, and the network is connected, we prove that
agents eventually learn the true parameter using a randomized gossip scheme. We
demonstrate that with high probability the convergence is exponentially fast
with a rate dependent on the KL divergence of observations under the true state
from observations under the second likeliest state. Furthermore, our work also
highlights the possibility of learning under continuous adaptation of network
which is a consequence of employing constant, unit stepsize for the algorithm.Comment: 6 pages, To appear in Conference on Decision and Control 201
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