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Article Dans Une Revue IEEE Transactions on Information Theory Année : 2013

Performance of a Distributed Stochastic Approximation Algorithm

Résumé

In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each node in a network updates a local estimate using a stochastic approximation algorithm with decreasing step size, and a gossip step, where a node computes a local weighted average between its estimates and those of its neighbors. Convergence of the estimates toward a consensus is established under weak assumptions. The approach relies on two main ingredients: the existence of a Lyapunov function for the mean field in the agreement subspace, and a contraction property of the random matrices of weights in the subspace orthogonal to the agreement subspace. A second-order analysis of the algorithm is also performed under the form of a central limit Theorem. The Polyak-averaged version of the algorithm is also considered.

Dates et versions

hal-02286437 , version 1 (13-09-2019)

Identifiants

Citer

P. Bianchi, Gersende Fort, Walid Hachem. Performance of a Distributed Stochastic Approximation Algorithm. IEEE Transactions on Information Theory, 2013, 59 (11), pp.7405-7418. ⟨10.1109/TIT.2013.2275131⟩. ⟨hal-02286437⟩
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