6,939 research outputs found
Optimization and Analysis of Distributed Averaging with Short Node Memory
In this paper, we demonstrate, both theoretically and by numerical examples,
that adding a local prediction component to the update rule can significantly
improve the convergence rate of distributed averaging algorithms. We focus on
the case where the local predictor is a linear combination of the node's two
previous values (i.e., two memory taps), and our update rule computes a
combination of the predictor and the usual weighted linear combination of
values received from neighbouring nodes. We derive the optimal mixing parameter
for combining the predictor with the neighbors' values, and carry out a
theoretical analysis of the improvement in convergence rate that can be
obtained using this acceleration methodology. For a chain topology on n nodes,
this leads to a factor of n improvement over the one-step algorithm, and for a
two-dimensional grid, our approach achieves a factor of n^1/2 improvement, in
terms of the number of iterations required to reach a prescribed level of
accuracy
Fast distributed estimation of empirical mass functions over anonymous networks
The aggregation and estimation of values over networks is fundamental for distributed applications, such as wireless sensor networks. Estimating the average, minimal and maximal values has already been extensively studied in the literature. In this paper, we focus on estimating empirical distributions of values in a network with anonymous agents. In particular, we compare two different estimation strategies in terms of their convergence speed, accuracy and communication costs. The first strategy is deterministic and based on the average consensus protocol, while the second strategy is probabilistic and based on the max consensus protocol
D-SVM over Networked Systems with Non-Ideal Linking Conditions
This paper considers distributed optimization algorithms, with application in
binary classification via distributed support-vector-machines (D-SVM) over
multi-agent networks subject to some link nonlinearities. The agents solve a
consensus-constraint distributed optimization cooperatively via continuous-time
dynamics, while the links are subject to strongly sign-preserving odd nonlinear
conditions. Logarithmic quantization and clipping (saturation) are two examples
of such nonlinearities. In contrast to existing literature that mostly
considers ideal links and perfect information exchange over linear channels, we
show how general sector-bounded models affect the convergence to the optimizer
(i.e., the SVM classifier) over dynamic balanced directed networks. In general,
any odd sector-bounded nonlinear mapping can be applied to our dynamics. The
main challenge is to show that the proposed system dynamics always have one
zero eigenvalue (associated with the consensus) and the other eigenvalues all
have negative real parts. This is done by recalling arguments from matrix
perturbation theory. Then, the solution is shown to converge to the agreement
state under certain conditions. For example, the gradient tracking (GT) step
size is tighter than the linear case by factors related to the upper/lower
sector bounds. To the best of our knowledge, no existing work in distributed
optimization and learning literature considers non-ideal link conditions
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