3,673 research outputs found
Design and Analysis of Distributed Averaging with Quantized Communication
Consider a network whose nodes have some initial values, and it is desired to
design an algorithm that builds on neighbor to neighbor interactions with the
ultimate goal of convergence to the average of all initial node values or to
some value close to that average. Such an algorithm is called generically
"distributed averaging," and our goal in this paper is to study the performance
of a subclass of deterministic distributed averaging algorithms where the
information exchange between neighboring nodes (agents) is subject to uniform
quantization. With such quantization, convergence to the precise average cannot
be achieved in general, but the convergence would be to some value close to it,
called quantized consensus. Using Lyapunov stability analysis, we characterize
the convergence properties of the resulting nonlinear quantized system. We show
that in finite time and depending on initial conditions, the algorithm will
either cause all agents to reach a quantized consensus where the consensus
value is the largest quantized value not greater than the average of their
initial values, or will lead all variables to cycle in a small neighborhood
around the average. In the latter case, we identify tight bounds for the size
of the neighborhood and we further show that the error can be made arbitrarily
small by adjusting the algorithm's parameters in a distributed manner
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
Fast Discrete Consensus Based on Gossip for Makespan Minimization in Networked Systems
In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip-like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O(n) in both theoretical and empirical comparisons
Nested Distributed Gradient Methods with Adaptive Quantized Communication
In this paper, we consider minimizing a sum of local convex objective
functions in a distributed setting, where communication can be costly. We
propose and analyze a class of nested distributed gradient methods with
adaptive quantized communication (NEAR-DGD+Q). We show the effect of performing
multiple quantized communication steps on the rate of convergence and on the
size of the neighborhood of convergence, and prove R-Linear convergence to the
exact solution with increasing number of consensus steps and adaptive
quantization. We test the performance of the method, as well as some practical
variants, on quadratic functions, and show the effects of multiple quantized
communication steps in terms of iterations/gradient evaluations, communication
and cost.Comment: 9 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1709.0299
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