Regime-Switching Langevin Monte Carlo Algorithms
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914015274336256 |
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| author | Wang, Xiaoyu Wang, Yingli Zhu, Lingjiong |
| author_facet | Wang, Xiaoyu Wang, Yingli Zhu, Lingjiong |
| contents | Langevin Monte Carlo (LMC) algorithms are popular Markov Chain Monte Carlo (MCMC) methods to sample a target probability distribution, which arises in many applications in machine learning. Inspired by regime-switching stochastic differential equations in the probability literature, we propose and study regime-switching Langevin dynamics (RS-LD) and regime-switching kinetic Langevin dynamics (RS-KLD). Based on their discretizations, we introduce regime-switching Langevin Monte Carlo (RS-LMC) and regime-switching kinetic Langevin Monte Carlo (RS-KLMC) algorithms, which can also be viewed as LMC and KLMC algorithms with random stepsizes. We also propose frictional-regime-switching kinetic Langevin dynamics (FRS-KLD) and its associated algorithm frictional-regime-switching kinetic Langevin Monte Carlo (FRS-KLMC), which can also be viewed as the KLMC algorithm with random frictional coefficients. We provide their 2-Wasserstein non-asymptotic convergence guarantees to the target distribution, and analyze the iteration complexities. Numerical experiments using both synthetic and real data are provided to illustrate the efficiency of our proposed algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regime-Switching Langevin Monte Carlo Algorithms Wang, Xiaoyu Wang, Yingli Zhu, Lingjiong Computation Machine Learning Probability Langevin Monte Carlo (LMC) algorithms are popular Markov Chain Monte Carlo (MCMC) methods to sample a target probability distribution, which arises in many applications in machine learning. Inspired by regime-switching stochastic differential equations in the probability literature, we propose and study regime-switching Langevin dynamics (RS-LD) and regime-switching kinetic Langevin dynamics (RS-KLD). Based on their discretizations, we introduce regime-switching Langevin Monte Carlo (RS-LMC) and regime-switching kinetic Langevin Monte Carlo (RS-KLMC) algorithms, which can also be viewed as LMC and KLMC algorithms with random stepsizes. We also propose frictional-regime-switching kinetic Langevin dynamics (FRS-KLD) and its associated algorithm frictional-regime-switching kinetic Langevin Monte Carlo (FRS-KLMC), which can also be viewed as the KLMC algorithm with random frictional coefficients. We provide their 2-Wasserstein non-asymptotic convergence guarantees to the target distribution, and analyze the iteration complexities. Numerical experiments using both synthetic and real data are provided to illustrate the efficiency of our proposed algorithms. |
| title | Regime-Switching Langevin Monte Carlo Algorithms |
| topic | Computation Machine Learning Probability |
| url | https://arxiv.org/abs/2509.00941 |