Stochastic subgradient algorithms for strongly convex optimization over distributed networks

Date
2017
Authors
Sayin, M. O.
Vanli, N. D.
Kozat, S. S.
Başar, T.
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
IEEE Transactions on Network Science and Engineering
Print ISSN
2327-4697
Electronic ISSN
Publisher
IEEE Computer Society
Volume
4
Issue
4
Pages
248 - 260
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Series
Abstract

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a different node; and a limited number of gradient oracle calls is allowed at each node. In this framework, we introduce a convex optimization algorithm based on stochastic subgradient descent (SSD) updates. We use a carefully designed time-dependent weighted averaging of the SSD iterates, which yields a convergence rate of O N ffiffiffi N p (1s)T after T gradient updates for each node on a network of N nodes, where 0 ≤ σ < 1 denotes the second largest singular value of the communication matrix. This rate of convergence matches the performance lower bound up to constant terms. Similar to the SSD algorithm, the computational complexity of the proposed algorithm also scales linearly with the dimensionality of the data. Furthermore, the communication load of the proposed method is the same as the communication load of the SSD algorithm. Thus, the proposed algorithm is highly efficient in terms of complexity and communication load. We illustrate the merits of the algorithm with respect to the state-of-art methods over benchmark real life data sets. © 2017 IEEE.

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Book Title
Keywords
Consensus strategies, Convex optimization, Diffusion strategies, Distributed processing, Online learning
Citation
Published Version (Please cite this version)