提出可随机切换步长的改进型采样算法，提升采样效率。
Regime-Switching Langevin Monte Carlo Algorithms
- 引入随机切换机制，让算法自适应调整步长或摩擦系数。
- 理论证明算法在2-沃瑟斯坦距离下收敛，给出迭代复杂度分析。
- 适合需要高效采样的机器学习任务，如贝叶斯推断与生成模型。
Langevin Monte Carlo（LMC）算法是机器学习中广泛使用的马尔可夫链蒙特卡罗方法，用于从目标概率分布采样。受概率论中状态切换随机微分方程的启发，本文提出并研究了状态切换Langevin动力学（RS-LD）和状态切换动能Langevin动力学（RS-KLD）。基于其离散化，引入状态切换LMC（RS-LMC）和状态切换动能LMC（RS-KLMC）算法，这些算法可视为具有随机步长的LMC与KLMC。同时提出带摩擦力的状态切换动能动力学（FRS-KLD）及其对应的算法FRS-KLMC，可视为具有随机摩擦系数的KLMC。本文提供了算法到目标分布的2-沃瑟斯坦距离非渐近收敛保证，并分析了迭代复杂度。通过合成数据和真实数据的数值实验，验证了所提算法的高效性。
原文摘要 · Abstract (English)
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.
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