10 research outputs found
Nonlinear Gossip Algorithms for Wireless Sensor Networks
We study some nonlinear gossip algorithms for wireless sensor networks. Firstly, two types of nonlinear single gossip algorithms are proposed. By using Lyapunov theory, Lagrange mean value theorem, and stochastic Lasalle’s invariance principle, we prove that the nonlinear single gossip algorithms can converge to the average of initial states with probability one. Secondly, two types of nonlinear multigossip algorithms are also presented and the convergence is proved by the same methods. Finally, computer simulation is also given to show the validity of the theoretical results
A Concentration Bound for Distributed Stochastic Approximation
We revisit the classical model of Tsitsiklis, Bertsekas and Athans for
distributed stochastic approximation with consensus. The main result is an
analysis of this scheme using the ODE approach to stochastic approximation,
leading to a high probability bound for the tracking error between suitably
interpolated iterates and the limiting differential equation. Several future
directions will also be highlighted
NONLINEAR GOSSIP
We consider a gossip-based distributed stochastic approximation scheme wherein processors situated at the nodes of a connected graph perform stochastic approximation algorithms, modified further by an additive interaction term equal to a weighted average of iterates at neighboring nodes along the lines of "gossip" algorithms. We allow these averaging weights to be modulated by the iterates themselves. The main result is a Benaim-type meta-theorem characterizing the possible asymptotic behavior in terms of a limiting o.d.e. In particular, this ensures "consensus," which we further strengthen to a form of "dynamic consensus" which implies that they asymptotically track a single common trajectory belonging to an internally chain transitive invariant set of a common o.d.e. that we characterize. We also consider a situation where this averaging is replaced by a fully nonlinear operation and extend the results to this case, which in particular allows us to handle certain projection schemes