Distributed Mismatch Tracking Algorithm for Constraint-Coupled Resource Allocation: Optimality and Differential Privacy
This paper considers constraint-coupled distributed resource allocation problems (DRAPs), where each agent holds a private cost function and obtains the solution via only local communication. In this paper, we propose a novel distributed algorithm (termed DMAC) to achieve optimality for DRAPs based...
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| Vydané v: | IEEE transactions on automatic control s. 1 - 15 |
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| Médium: | Journal Article |
| Jazyk: | English |
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| ISSN: | 0018-9286, 1558-2523 |
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| Abstract | This paper considers constraint-coupled distributed resource allocation problems (DRAPs), where each agent holds a private cost function and obtains the solution via only local communication. In this paper, we propose a novel distributed algorithm (termed DMAC) to achieve optimality for DRAPs based on mismatch tracking scheme. We show that the proposed algorithm converges at a sublinear rate for strongly convex cost functions and a linear convergence rate for smooth and strongly convex cost functions, respectively. With privacy concerns, the exchanged information is masked with independent Laplace noise against potential attackers with access to even all network communication. We further propose a differentially private version (termed diff-DMAC) to achieve cost-optimal distribution of resources while preserving privacy. Adopting constant stepsizes, the linear convergence property of diff-DMAC in mean square is established. Moreover, it is proven that the algorithm is differentially private. We also characterize and improve the trade-off between convergence accuracy and privacy level. Finally, a numerical example is provided for verification. |
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| AbstractList | This paper considers constraint-coupled distributed resource allocation problems (DRAPs), where each agent holds a private cost function and obtains the solution via only local communication. In this paper, we propose a novel distributed algorithm (termed DMAC) to achieve optimality for DRAPs based on mismatch tracking scheme. We show that the proposed algorithm converges at a sublinear rate for strongly convex cost functions and a linear convergence rate for smooth and strongly convex cost functions, respectively. With privacy concerns, the exchanged information is masked with independent Laplace noise against potential attackers with access to even all network communication. We further propose a differentially private version (termed diff-DMAC) to achieve cost-optimal distribution of resources while preserving privacy. Adopting constant stepsizes, the linear convergence property of diff-DMAC in mean square is established. Moreover, it is proven that the algorithm is differentially private. We also characterize and improve the trade-off between convergence accuracy and privacy level. Finally, a numerical example is provided for verification. |
| Author | Zhu, Shanying Guan, Xinping Liu, Shuai Wu, Wenwen |
| Author_xml | – sequence: 1 givenname: Wenwen surname: Wu fullname: Wu, Wenwen email: wuwenwen@sjtu.edu.cn organization: School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai, China – sequence: 2 givenname: Shanying surname: Zhu fullname: Zhu, Shanying email: shyingzhu@gmail.com organization: School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai, China – sequence: 3 givenname: Shuai surname: Liu fullname: Liu, Shuai email: LIUS0025@ntu.edu.sg organization: School of Control Science and Engineering, Shandong University, Jinan, China – sequence: 4 givenname: Xinping surname: Guan fullname: Guan, Xinping email: xpguan@sjtu.edu.cn organization: School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai, China |
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| SubjectTerms | Differential privacy distributed optimization multi-agent systems optimization algorithms |
| Title | Distributed Mismatch Tracking Algorithm for Constraint-Coupled Resource Allocation: Optimality and Differential Privacy |
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