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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Veröffentlicht in:	IEEE transactions on automatic control Jg. 65; H. 6; S. 2494 - 2509
Hauptverfasser:	Zhang, Jiaqi, You, Keyou
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.06.2020 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	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
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Abstract	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.
AbstractList	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.
Author	Zhang, Jiaqi You, Keyou
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SubjectTerms	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)
Title	AsySPA: An Exact Asynchronous Algorithm for Convex Optimization Over Digraphs
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