10,499 research outputs found
Distributed Constrained Recursive Nonlinear Least-Squares Estimation: Algorithms and Asymptotics
This paper focuses on the problem of recursive nonlinear least squares
parameter estimation in multi-agent networks, in which the individual agents
observe sequentially over time an independent and identically distributed
(i.i.d.) time-series consisting of a nonlinear function of the true but unknown
parameter corrupted by noise. A distributed recursive estimator of the
\emph{consensus} + \emph{innovations} type, namely , is
proposed, in which the agents update their parameter estimates at each
observation sampling epoch in a collaborative way by simultaneously processing
the latest locally sensed information~(\emph{innovations}) and the parameter
estimates from other agents~(\emph{consensus}) in the local neighborhood
conforming to a pre-specified inter-agent communication topology. Under rather
weak conditions on the connectivity of the inter-agent communication and a
\emph{global observability} criterion, it is shown that at every network agent,
the proposed algorithm leads to consistent parameter estimates. Furthermore,
under standard smoothness assumptions on the local observation functions, the
distributed estimator is shown to yield order-optimal convergence rates, i.e.,
as far as the order of pathwise convergence is concerned, the local parameter
estimates at each agent are as good as the optimal centralized nonlinear least
squares estimator which would require access to all the observations across all
the agents at all times. In order to benchmark the performance of the proposed
distributed estimator with that of the centralized nonlinear
least squares estimator, the asymptotic normality of the estimate sequence is
established and the asymptotic covariance of the distributed estimator is
evaluated. Finally, simulation results are presented which illustrate and
verify the analytical findings.Comment: 28 pages. Initial Submission: Feb. 2016, Revised: July 2016,
Accepted: September 2016, To appear in IEEE Transactions on Signal and
Information Processing over Networks: Special Issue on Inference and Learning
over Network
Distributed Delayed Stochastic Optimization
We analyze the convergence of gradient-based optimization algorithms that
base their updates on delayed stochastic gradient information. The main
application of our results is to the development of gradient-based distributed
optimization algorithms where a master node performs parameter updates while
worker nodes compute stochastic gradients based on local information in
parallel, which may give rise to delays due to asynchrony. We take motivation
from statistical problems where the size of the data is so large that it cannot
fit on one computer; with the advent of huge datasets in biology, astronomy,
and the internet, such problems are now common. Our main contribution is to
show that for smooth stochastic problems, the delays are asymptotically
negligible and we can achieve order-optimal convergence results. In application
to distributed optimization, we develop procedures that overcome communication
bottlenecks and synchronization requirements. We show -node architectures
whose optimization error in stochastic problems---in spite of asynchronous
delays---scales asymptotically as \order(1 / \sqrt{nT}) after iterations.
This rate is known to be optimal for a distributed system with nodes even
in the absence of delays. We additionally complement our theoretical results
with numerical experiments on a statistical machine learning task.Comment: 27 pages, 4 figure
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