AsySPA: An Exact Asynchronous Algorithm for Convex Optimization Over Digraphs

This paper proposes a novel exact asynchronous subgradient-push algorithm (AsySPA) to solve an additive cost optimization problem over digraphs where each node only has access to a local convex function and updates asynchronously with an arbitrary rate. Specifically, each node of a strongly connecte...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 65; no. 6; pp. 2494 - 2509
Main Authors: Zhang, Jiaqi, You, Keyou
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Asynchronous subgradient-push algorithm (AsySPA)
Clocks
Computational geometry
Computer simulation
Convergence
Convex functions
Convexity
Delays
Distributed algorithms
distributed optimization problem (DOP)
even update rates (EUR)
Graph theory
Nodes
Optimization
Synchronization
uneven update rates (UUR)
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:This paper proposes a novel exact asynchronous subgradient-push algorithm (AsySPA) to solve an additive cost optimization problem over digraphs where each node only has access to a local convex function and updates asynchronously with an arbitrary rate. Specifically, each node of a strongly connected digraph does not wait for updates from other nodes but simply starts a new update within any bounded time interval by using local information available from its in-neighbors. "Exact" means that every node of the AsySPA can asymptotically converge to the same optimal solution, even under different update rates among nodes and bounded communication delays. To address uneven update rates, we design a simple mechanism to adaptively adjust stepsizes per update in each node, which is substantially different from the existing works. Then, we construct a delay-free augmented system to address asynchrony and delays, and study its convergence by proposing a generalized subgradient algorithm, which clearly has its own significance and helps us to explicitly evaluate the convergence rate of the AsySPA. Finally, we demonstrate advantages of the AsySPA in both theory and simulation.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2019.2930234