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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.02766 |
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| _version_ | 1866911818643931136 |
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| author | Lu, Liwei Guo, Hailong Yang, Xu Zhu, Yi |
| author_facet | Lu, Liwei Guo, Hailong Yang, Xu Zhu, Yi |
| contents | In this paper, we propose a deep learning framework for solving high-dimensional partial integro-differential equations (PIDEs) based on the temporal difference learning. We introduce a set of Levy processes and construct a corresponding reinforcement learning model. To simulate the entire process, we use deep neural networks to represent the solutions and non-local terms of the equations. Subsequently, we train the networks using the temporal difference error, termination condition, and properties of the non-local terms as the loss function. The relative error of the method reaches O(10^{-3}) in 100-dimensional experiments and O(10^{-4}) in one-dimensional pure jump problems. Additionally, our method demonstrates the advantages of low computational cost and robustness, making it well-suited for addressing problems with different forms and intensities of jumps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02766 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Temporal Difference Learning for High-Dimensional PIDEs with Jumps Lu, Liwei Guo, Hailong Yang, Xu Zhu, Yi Numerical Analysis Machine Learning In this paper, we propose a deep learning framework for solving high-dimensional partial integro-differential equations (PIDEs) based on the temporal difference learning. We introduce a set of Levy processes and construct a corresponding reinforcement learning model. To simulate the entire process, we use deep neural networks to represent the solutions and non-local terms of the equations. Subsequently, we train the networks using the temporal difference error, termination condition, and properties of the non-local terms as the loss function. The relative error of the method reaches O(10^{-3}) in 100-dimensional experiments and O(10^{-4}) in one-dimensional pure jump problems. Additionally, our method demonstrates the advantages of low computational cost and robustness, making it well-suited for addressing problems with different forms and intensities of jumps. |
| title | Temporal Difference Learning for High-Dimensional PIDEs with Jumps |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2307.02766 |