Solution Theory of Hamilton-Jacobi-Bellman Equations in Spectral Barron Spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909791480184832 |
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| author | Feng, Ye Lu, Jianfeng |
| author_facet | Feng, Ye Lu, Jianfeng |
| contents | We study the solution theory of the whole-space static (elliptic) Hamilton-Jacobi-Bellman (HJB) equation in spectral Barron spaces. We prove that under the assumption that the coefficients involved are spectral Barron functions and the discount factor is sufficiently large, there exists a sequence of uniformly bounded spectral Barron functions that converges locally uniformly to the solution. As a consequence, the solution of the HJB equation can be approximated by two-layer neural networks without curse of dimensionality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solution Theory of Hamilton-Jacobi-Bellman Equations in Spectral Barron Spaces Feng, Ye Lu, Jianfeng Analysis of PDEs We study the solution theory of the whole-space static (elliptic) Hamilton-Jacobi-Bellman (HJB) equation in spectral Barron spaces. We prove that under the assumption that the coefficients involved are spectral Barron functions and the discount factor is sufficiently large, there exists a sequence of uniformly bounded spectral Barron functions that converges locally uniformly to the solution. As a consequence, the solution of the HJB equation can be approximated by two-layer neural networks without curse of dimensionality. |
| title | Solution Theory of Hamilton-Jacobi-Bellman Equations in Spectral Barron Spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.18656 |