Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped Langevin dynamics. There are many variants of Langevin dynamics that often show superior performance in practice. In this paper, we provide a unified approach to study the acceleration of the variants of the overdamped Langevin dynamics through the lens of large deviations theory. Numerical experiments using both synthetic and real data are provided to illustrate the efficiency of these variants.

翻译：朗之万算法是流行的马尔可夫链蒙特卡洛方法，常被用于解决机器学习中的高维大规模采样问题。最经典的朗之万蒙特卡洛算法基于过阻尼朗之万动力学。实际应用中，许多朗之万动力学的变体往往表现出更优越的性能。本文通过大偏差理论视角，为研究过阻尼朗之万动力学变体的加速问题提供了统一框架。我们基于合成数据与真实数据的数值实验，验证了这些变体的高效性。