An adaptive online learning algorithm for distributed convex optimization with coupled constraints over unbalanced directed graphs

This paper investigates a distributed optimization problem over multi-agent networks subject to both local and coupled constraints in a non-stationary environment, where a set of agents aim to cooperatively minimize the sum of locally time-varying cost functions when the communication graphs are tim...

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Published in:	Journal of the Franklin Institute Vol. 356; no. 13; pp. 7548 - 7570
Main Authors:	Gu, Chuanye, Li, Jueyou, Wu, Zhiyou
Format:	Journal Article
Language:	English
Published:	Elmsford Elsevier Ltd 01.09.2019 Elsevier Science Ltd
Subjects:	Adaptive algorithms Algorithms Computational geometry Computer simulation Convexity Coupling Electric vehicle charging Electric vehicles Graph theory Graphs Machine learning Multiagent systems Nonstationary environments Optimization Studies
ISSN:	0016-0032, 1879-2693, 0016-0032
Online Access:	Get full text
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Abstract	This paper investigates a distributed optimization problem over multi-agent networks subject to both local and coupled constraints in a non-stationary environment, where a set of agents aim to cooperatively minimize the sum of locally time-varying cost functions when the communication graphs are time-changing connected and unbalanced. Based on dual decomposition, we propose a distributed online dual push-sum learning algorithm by incorporating the push-sum protocol into dual gradient method. We then show that the regret bound has a sublinear growth of O(Tp) and the constraint violation is also sublinear with order of O(T1−p/2), where T is the time horizon and 0 < p ≤ 1/2. Finally, simulation experiments on a plug-in electric vehicle charging problem are utilized to verify the performance of the proposed algorithm. The proposed algorithm is adaptive without knowing the total number of iterations T in advance. The convergence results are established on more general unbalanced graphs without the boundedness assumption on dual variables. In addition, more privacy concerns are guaranteed since only dual variables related with coupled constraints are exchanged among agents.
AbstractList	This paper investigates a distributed optimization problem over multi-agent networks subject to both local and coupled constraints in a non-stationary environment, where a set of agents aim to cooperatively minimize the sum of locally time-varying cost functions when the communication graphs are time-changing connected and unbalanced. Based on dual decomposition, we propose a distributed online dual push-sum learning algorithm by incorporating the push-sum protocol into dual gradient method. We then show that the regret bound has a sublinear growth of O(Tp) and the constraint violation is also sublinear with order of O(T1−p/2), where T is the time horizon and 0 < p ≤ 1/2. Finally, simulation experiments on a plug-in electric vehicle charging problem are utilized to verify the performance of the proposed algorithm. The proposed algorithm is adaptive without knowing the total number of iterations T in advance. The convergence results are established on more general unbalanced graphs without the boundedness assumption on dual variables. In addition, more privacy concerns are guaranteed since only dual variables related with coupled constraints are exchanged among agents.
Author	Wu, Zhiyou Gu, Chuanye Li, Jueyou
Author_xml	– sequence: 1 givenname: Chuanye surname: Gu fullname: Gu, Chuanye email: chuanye.gu@postgrad.curtin.edu.au organization: Department of Mathematics and Statistics, Cutin University, Perth, WA 6845, Australia – sequence: 2 givenname: Jueyou surname: Li fullname: Li, Jueyou email: lijueyou@cqnu.edu.cn organization: School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China – sequence: 3 givenname: Zhiyou surname: Wu fullname: Wu, Zhiyou email: zywu@cqnu.edu.cn organization: School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China
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Snippet	This paper investigates a distributed optimization problem over multi-agent networks subject to both local and coupled constraints in a non-stationary...
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SubjectTerms	Adaptive algorithms Algorithms Computational geometry Computer simulation Convexity Coupling Electric vehicle charging Electric vehicles Graph theory Graphs Machine learning Multiagent systems Nonstationary environments Optimization Studies
Title	An adaptive online learning algorithm for distributed convex optimization with coupled constraints over unbalanced directed graphs
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