期刊
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
卷 54, 期 3, 页码 1535-1557出版社
SIAM PUBLICATIONS
DOI: 10.1137/140992588
关键词
gossip algorithms; distributed algorithms; stochastic approximation; two time scales; Benaim theorem
资金
- J. C. Bose Fellowship
- Department of Science and Technology, Government of India
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.
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