43,955 research outputs found
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
Quantization Design for Distributed Optimization
We consider the problem of solving a distributed optimization problem using a
distributed computing platform, where the communication in the network is
limited: each node can only communicate with its neighbours and the channel has
a limited data-rate. A common technique to address the latter limitation is to
apply quantization to the exchanged information. We propose two distributed
optimization algorithms with an iteratively refining quantization design based
on the inexact proximal gradient method and its accelerated variant. We show
that if the parameters of the quantizers, i.e. the number of bits and the
initial quantization intervals, satisfy certain conditions, then the
quantization error is bounded by a linearly decreasing function and the
convergence of the distributed algorithms is guaranteed. Furthermore, we prove
that after imposing the quantization scheme, the distributed algorithms still
exhibit a linear convergence rate, and show complexity upper-bounds on the
number of iterations to achieve a given accuracy. Finally, we demonstrate the
performance of the proposed algorithms and the theoretical findings for solving
a distributed optimal control problem
FAASTA: A fast solver for total-variation regularization of ill-conditioned problems with application to brain imaging
The total variation (TV) penalty, as many other analysis-sparsity problems,
does not lead to separable factors or a proximal operatorwith a closed-form
expression, such as soft thresholding for the penalty. As a result,
in a variational formulation of an inverse problem or statisticallearning
estimation, it leads to challenging non-smooth optimization problemsthat are
often solved with elaborate single-step first-order methods. When thedata-fit
term arises from empirical measurements, as in brain imaging, it isoften very
ill-conditioned and without simple structure. In this situation, in proximal
splitting methods, the computation cost of thegradient step can easily dominate
each iteration. Thus it is beneficialto minimize the number of gradient
steps.We present fAASTA, a variant of FISTA, that relies on an internal solver
forthe TV proximal operator, and refines its tolerance to balance
computationalcost of the gradient and the proximal steps. We give benchmarks
andillustrations on "brain decoding": recovering brain maps from
noisymeasurements to predict observed behavior. The algorithm as well as
theempirical study of convergence speed are valuable for any non-exact
proximaloperator, in particular analysis-sparsity problems
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