Convergence in total variation for the kinetic Langevin algorithm
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-kin...
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| Vydáno v: | Mathematical statistics and learning (Online) Ročník 8; číslo 1; s. 71 - 104 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
21.08.2025
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| ISSN: | 2520-2316, 2520-2324 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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}) . |
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| ISSN: | 2520-2316 2520-2324 |
| DOI: | 10.4171/msl/49 |