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Performance of a Distributed Stochastic Approximation Algorithm

P. Bianchi 1, 2 Gersende Fort 1, 2 Walid Hachem 3, 4 
1 S2A - Signal, Statistique et Apprentissage
LTCI - Laboratoire Traitement et Communication de l'Information
3 COMNUM - Communications Numériques
LTCI - Laboratoire Traitement et Communication de l'Information
Abstract : 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.
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Submitted on : Friday, September 13, 2019 - 3:44:45 PM
Last modification on : Monday, March 14, 2022 - 3:03:56 PM

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



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