Convergence in total variation for the kinetic Langevin algorithm
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915195628027904 |
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| author | Lehec, Joseph |
| author_facet | Lehec, Joseph |
| contents | We prove non asymptotic total variation estimates for the kinetic Langevin algorithm in high dimension when the target measure satisfies a Poincaré inequality and has gradient Lipschitz potential. The main point is that the estimate improves significantly upon the corresponding bound for the non kinetic version of the algorithm, due to Dalalyan. In particular the dimension dependence drops from $O(n)$ to $O(\sqrt n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09301 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence in total variation for the kinetic Langevin algorithm Lehec, Joseph Probability Computational Complexity Analysis of PDEs 35H10, 65C05, 68W20 We prove non asymptotic total variation estimates for the kinetic Langevin algorithm in high dimension when the target measure satisfies a Poincaré inequality and has gradient Lipschitz potential. The main point is that the estimate improves significantly upon the corresponding bound for the non kinetic version of the algorithm, due to Dalalyan. In particular the dimension dependence drops from $O(n)$ to $O(\sqrt n)$. |
| title | Convergence in total variation for the kinetic Langevin algorithm |
| topic | Probability Computational Complexity Analysis of PDEs 35H10, 65C05, 68W20 |
| url | https://arxiv.org/abs/2407.09301 |