Institute of Electrical & Electronic Engineers
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.