Distributed Fractional Bayesian Learning for Adaptive Optimization
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912560581705728 |
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| author | Yang, Yaqun Lei, Jinlong Wen, Guanghui Hong, Yiguang |
| author_facet | Yang, Yaqun Lei, Jinlong Wen, Guanghui Hong, Yiguang |
| contents | This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter, whereas they mean to collaboratively estimate the true parameter and find the optimal solution over a connected network. A general mathematical framework for such a problem has not been studied yet. We aim to provide valuable insights for addressing parameter uncertainty in distributed optimization problems and simultaneously find the optimal solution. Thus, we propose a novel distributed scheme, which utilizes distributed fractional Bayesian learning through weighted averaging on the log-beliefs to update the beliefs of unknown parameter, and distributed gradient descent for renewing the estimation of the optimal solution. Then under suitable assumptions, we prove that all agents' beliefs and decision variables converge almost surely to the true parameter and the optimal solution under the true parameter, respectively. We further establish a sublinear convergence rate for the belief sequence. Finally, numerical experiments are implemented to corroborate the theoretical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributed Fractional Bayesian Learning for Adaptive Optimization Yang, Yaqun Lei, Jinlong Wen, Guanghui Hong, Yiguang Optimization and Control Distributed, Parallel, and Cluster Computing Machine Learning Multiagent Systems This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter, whereas they mean to collaboratively estimate the true parameter and find the optimal solution over a connected network. A general mathematical framework for such a problem has not been studied yet. We aim to provide valuable insights for addressing parameter uncertainty in distributed optimization problems and simultaneously find the optimal solution. Thus, we propose a novel distributed scheme, which utilizes distributed fractional Bayesian learning through weighted averaging on the log-beliefs to update the beliefs of unknown parameter, and distributed gradient descent for renewing the estimation of the optimal solution. Then under suitable assumptions, we prove that all agents' beliefs and decision variables converge almost surely to the true parameter and the optimal solution under the true parameter, respectively. We further establish a sublinear convergence rate for the belief sequence. Finally, numerical experiments are implemented to corroborate the theoretical analysis. |
| title | Distributed Fractional Bayesian Learning for Adaptive Optimization |
| topic | Optimization and Control Distributed, Parallel, and Cluster Computing Machine Learning Multiagent Systems |
| url | https://arxiv.org/abs/2404.11354 |