The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is sometimes high because each iteration requires the computation of a gradient. One approach to eliminate the gradient computation is to employ the concept of "ensemble". A large number of particles are evolved together so the neighboring particles provide gradient information to each other. In this article, we discuss two algorithms that integrate the ensemble feature into LMC and the associated properties. In particular, we find that if one directly surrogates the gradient using the ensemble approximation, the algorithm, termed Ensemble Langevin Monte Carlo, is unstable due to a high variance term. If the gradients are replaced by the ensemble approximations only in a constrained manner, to protect from the unstable points, the algorithm, termed Constrained Ensemble Langevin Monte Carlo, resembles the classical LMC up to an ensemble error but removes most of the gradient computation.

翻译：古典的 Langevin Monte Carlo 方法通过在目标分布梯度上降低样本,寻找目标分布的样本。 方法具有快速趋同率。 但是, 数字成本有时很高, 因为每次迭代都需要计算梯度。 消除梯度计算的方法之一是使用“ 共性” 的概念。 许多粒子是一起演进的, 这样相邻的粒子可以相互提供梯度信息。 在文章中, 我们讨论两种将共性特性纳入 LMC 和相关属性的算法。 特别是, 我们发现, 如果使用共性近似直接代用梯度, 算法, 称为 Ensemble Langevin Monte Carlo 的算法是不稳定的。 如果梯度仅以制约的方式被共性近似值所取代, 用于保护不稳定点的算法, 被称为 Consstrated Ensemble Langevin Monte Carlo 的算法, 类似于经典的经典 LMC, 和一个共性误差, 但是排除了大部分梯度计算。