Distributed learning with multi-penalty regularization |
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Authors: | Zheng-Chu Guo Shao-Bo Lin Lei Shi |
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Affiliation: | 1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China;2. Department of Statistics, Wenzhou University, Wenzhou, 325035, China;3. Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, 200433, China |
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Abstract: | In this paper, we study distributed learning with multi-penalty regularization based on a divide-and-conquer approach. Using Neumann expansion and a second order decomposition on difference of operator inverses approach, we derive optimal learning rates for distributed multi-penalty regularization in expectation. As a byproduct, we also deduce optimal learning rates for multi-penalty regularization, which was not given in the literature. These results are applied to the distributed manifold regularization and optimal learning rates are given. |
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Keywords: | Learning theory Multi-penalty regularization Manifold regularization Integral operator |
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