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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.00342 |
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| _version_ | 1866918224121036800 |
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| author | Li, Haizheng Guo, Lei |
| author_facet | Li, Haizheng Guo, Lei |
| contents | Real-world intelligence systems usually operate by combining offline learning and online adaptation with highly correlated and non-stationary system data or signals, which, however, has rarely been investigated theoretically in the literature. This paper initiates a theoretical investigation on the prediction performance of a two-stage learning framework combining offline and online algorithms for a class of nonlinear stochastic dynamical systems. For the offline-learning phase, we establish an upper bound on the generalization error for approximate nonlinear-least-squares estimation under general datasets with strong correlation and distribution shift, leveraging the Kullback-Leibler divergence to quantify the distributional discrepancies. For the online-adaptation phase, we address, on the basis of the offline-trained model, the possible uncertain parameter drift in real-world target systems by proposing a meta-LMS prediction algorithm. This two-stage framework, integrating offline learning with online adaptation, demonstrates superior prediction performances compared with either purely offline or online methods. Both theoretical guarantees and empirical studies are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive prediction theory combining offline and online learning Li, Haizheng Guo, Lei Machine Learning Systems and Control Real-world intelligence systems usually operate by combining offline learning and online adaptation with highly correlated and non-stationary system data or signals, which, however, has rarely been investigated theoretically in the literature. This paper initiates a theoretical investigation on the prediction performance of a two-stage learning framework combining offline and online algorithms for a class of nonlinear stochastic dynamical systems. For the offline-learning phase, we establish an upper bound on the generalization error for approximate nonlinear-least-squares estimation under general datasets with strong correlation and distribution shift, leveraging the Kullback-Leibler divergence to quantify the distributional discrepancies. For the online-adaptation phase, we address, on the basis of the offline-trained model, the possible uncertain parameter drift in real-world target systems by proposing a meta-LMS prediction algorithm. This two-stage framework, integrating offline learning with online adaptation, demonstrates superior prediction performances compared with either purely offline or online methods. Both theoretical guarantees and empirical studies are provided. |
| title | Adaptive prediction theory combining offline and online learning |
| topic | Machine Learning Systems and Control |
| url | https://arxiv.org/abs/2512.00342 |