Convergence rate of randomized midpoint Langevin Monte Carlo
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909908016824320 |
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| author | Li, Ruinan Shen, Tian Su, Zhonggen |
| author_facet | Li, Ruinan Shen, Tian Su, Zhonggen |
| contents | The randomized midpoint Langevin Monte Carlo (RLMC), introduced by Shen and Lee (2019), is a variant of classical Unadjusted Langevin Algorithm. It was shown in the literature that the RLMC is an efficient algorithm for approximating high-dimensional probability distribution $π$. In this paper, we establish the exponential ergodicity of RLMC with constant step-size. Moreover, we design a dereasing-step size RLMC and provide its convergence rate in terms of a functional class distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13093 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence rate of randomized midpoint Langevin Monte Carlo Li, Ruinan Shen, Tian Su, Zhonggen Statistics Theory Probability The randomized midpoint Langevin Monte Carlo (RLMC), introduced by Shen and Lee (2019), is a variant of classical Unadjusted Langevin Algorithm. It was shown in the literature that the RLMC is an efficient algorithm for approximating high-dimensional probability distribution $π$. In this paper, we establish the exponential ergodicity of RLMC with constant step-size. Moreover, we design a dereasing-step size RLMC and provide its convergence rate in terms of a functional class distance. |
| title | Convergence rate of randomized midpoint Langevin Monte Carlo |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2511.13093 |