Stochastic Gradient-Push for Strongly Convex Functions on Time-Varying Directed Graphs

We investigate the convergence rate of the recently proposed subgradient-push method for distributed optimization over time-varying directed graphs. The subgradient-push method can be implemented in a distributed way without requiring knowledge of either the number of agents or the graph sequence; e...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 61; no. 12; pp. 3936 - 3947
Main Authors Nedic, Angelia, Olshevsky, Alex
Format Journal Article
LanguageEnglish
Published New York IEEE 01.12.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Convergence
Convex analysis
Convex functions
Distributed algorithms
gradient methods
Graph theory
Graphs
Markov processes
Noise measurement
Optimization
parameter estimation
Protocols
Time varying control
Topology
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Summary:We investigate the convergence rate of the recently proposed subgradient-push method for distributed optimization over time-varying directed graphs. The subgradient-push method can be implemented in a distributed way without requiring knowledge of either the number of agents or the graph sequence; each node is only required to know its out-degree at each time. Our main result is a convergence rate of O((ln t)/t) for strongly convex functions with Lipschitz gradients even if only stochastic gradient samples are available; this is asymptotically faster than the O((ln t)/√t) rate previously known for (general) convex functions.
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content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2016.2529285