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Communication Dans Un Congrès Année : 2014

Random pairwise gossip on CAT(0) metric spaces

Résumé

In the context of sensor networks, gossip algo-rithms are a popular, well established technique for achieving consensus when sensor data is encoded in Euclidean spaces. The algorithm also has several extensions to nonlinear data spaces. Most of these extensions deal with Riemannian data spaces and use gradient descent techniques to derive a generalization of the gossip algorithm. However, their heavy reliance on calculus tools hides the simple metric properties that make gossip algorithms work. This paper studies the pairwise gossip algorithm from a purely metric perspective. Focusing on the essential property that makes pairwise midpoint gossip converge on Riemannian manifolds, this paper argues that the notion of C AT (0) space is perfectly suited to the analysis of gossip algorithms. The transition from a Riemannian to a purely metrical framework has three virtues: it simplifies the proofs, provably preserves convergence speed of pairwise gossip, yet in a more general framework, and paves the way for new applications, as illustrated by our numerical experiments on robots arms viewed as points in the metric graph associated with the free group
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Dates et versions

hal-01257891 , version 1 (18-01-2016)

Identifiants

Citer

Anass Bellachehab, Jérémie Jakubowicz. Random pairwise gossip on CAT(0) metric spaces. CDC 2014 : 53rd IEEE Conference on Decision and Control , Dec 2014, Los Angeles, United States. pp.5593 - 5598 ⟨10.1109/CDC.2014.7040264⟩. ⟨hal-01257891⟩
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