Stochastic mirror descent method for distributed multi-agent optimization
© 2016 Springer-Verlag Berlin HeidelbergThis paper considers a distributed optimization problem encountered in a time-varying multi-agent network, where each agent has local access to its convex objective function, and cooperatively minimizes a sum of convex objective functions of the agents over th...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Springer Verlag
2016
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| Online Access: | http://hdl.handle.net/20.500.11937/4712 |
| _version_ | 1848744592823812096 |
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| author | Li, J. Li, G. Wu, Z. Wu, Changzhi |
| author_facet | Li, J. Li, G. Wu, Z. Wu, Changzhi |
| author_sort | Li, J. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2016 Springer-Verlag Berlin HeidelbergThis paper considers a distributed optimization problem encountered in a time-varying multi-agent network, where each agent has local access to its convex objective function, and cooperatively minimizes a sum of convex objective functions of the agents over the network. Based on the mirror descent method, we develop a distributed algorithm by utilizing the subgradient information with stochastic errors. We firstly analyze the effects of stochastic errors on the convergence of the algorithm and then provide an explicit bound on the convergence rate as a function of the error bound and number of iterations. Our results show that the algorithm asymptotically converges to the optimal value of the problem within an error level, when there are stochastic errors in the subgradient evaluations. The proposed algorithm can be viewed as a generalization of the distributed subgradient projection methods since it utilizes more general Bregman divergence instead of the Euclidean squared distance. Finally, some simulation results on a regularized hinge regression problem are presented to illustrate the effectiveness of the algorithm. |
| first_indexed | 2025-11-14T06:03:55Z |
| format | Journal Article |
| id | curtin-20.500.11937-4712 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:03:55Z |
| publishDate | 2016 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-47122017-09-13T14:44:36Z Stochastic mirror descent method for distributed multi-agent optimization Li, J. Li, G. Wu, Z. Wu, Changzhi © 2016 Springer-Verlag Berlin HeidelbergThis paper considers a distributed optimization problem encountered in a time-varying multi-agent network, where each agent has local access to its convex objective function, and cooperatively minimizes a sum of convex objective functions of the agents over the network. Based on the mirror descent method, we develop a distributed algorithm by utilizing the subgradient information with stochastic errors. We firstly analyze the effects of stochastic errors on the convergence of the algorithm and then provide an explicit bound on the convergence rate as a function of the error bound and number of iterations. Our results show that the algorithm asymptotically converges to the optimal value of the problem within an error level, when there are stochastic errors in the subgradient evaluations. The proposed algorithm can be viewed as a generalization of the distributed subgradient projection methods since it utilizes more general Bregman divergence instead of the Euclidean squared distance. Finally, some simulation results on a regularized hinge regression problem are presented to illustrate the effectiveness of the algorithm. 2016 Journal Article http://hdl.handle.net/20.500.11937/4712 10.1007/s11590-016-1071-z Springer Verlag restricted |
| spellingShingle | Li, J. Li, G. Wu, Z. Wu, Changzhi Stochastic mirror descent method for distributed multi-agent optimization |
| title | Stochastic mirror descent method for distributed multi-agent optimization |
| title_full | Stochastic mirror descent method for distributed multi-agent optimization |
| title_fullStr | Stochastic mirror descent method for distributed multi-agent optimization |
| title_full_unstemmed | Stochastic mirror descent method for distributed multi-agent optimization |
| title_short | Stochastic mirror descent method for distributed multi-agent optimization |
| title_sort | stochastic mirror descent method for distributed multi-agent optimization |
| url | http://hdl.handle.net/20.500.11937/4712 |