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https://open.uns.ac.rs/handle/123456789/585
Title: | Convergence Rates for Distributed Stochastic Optimization over Random Networks | Authors: | Jakovetić, Dušan Bajović, Dragana Sahu A. Kar S. |
Issue Date: | 18-Jan-2019 | Journal: | Proceedings of the IEEE Conference on Decision and Control | Abstract: | © 2018 IEEE. We establish the O(\frac{1}{k}) convergence rate for distributed stochastic gradient methods that operate over strongly convex costs and random networks. The considered class of methods is standard - each node performs a weighted average of its own and its neighbors' solution estimates (consensus), and takes a negative step with respect to a noisy version of its local function's gradient (innovation). The underlying communication network is modeled through a sequence of temporally independent identically distributed (i.i.d.) Laplacian matrices such that the underlying graphs are connected on average; the local gradient noises are also i.i.d. in time, have finite second moment, and possibly unbounded support. We show that, after a careful setting of the consensus and innovations potentials (weights), the distributed stochastic gradient method achieves a (order-optimal) O(\frac{1}{k}) convergence rate in the mean square distance from the solution. To the best of our knowledge, this is the first order-optimal convergence rate result on distributed strongly convex stochastic optimization when the network is random and the gradient noises have unbounded support. Simulation examples confirm the theoretical findings. | URI: | https://open.uns.ac.rs/handle/123456789/585 | ISBN: | 9781538613955 | ISSN: | 07431546 | DOI: | 10.1109/CDC.2018.8619228 |
Appears in Collections: | FTN Publikacije/Publications |
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