We prove non asymptotic polynomial bounds on the convergence of the Langevin Monte Carlo algorithm in the case where the potential is a convex function which is globally Lipschitz on its domain, typically the maximum of a finite number of affine functions on an arbitrary convex set. In particular the potential is not assumed to be gradient Lipschitz, in contrast with most (if not all) existing works on the topic.
翻译:在Langevin Monte Carlo算法合而为一的情况下,我们证明,在Langevin Monte Carlo算法的趋同方面,我们没有零星的多元界限,因为其潜力是全球范围内Lipschitz的 convex函数,通常是在任意的 convex 集上最多有一定数目的同系函数,尤其是,与大多数(如果不是全部的话)关于这个专题的现有工作相比,其潜力并不被认为是梯度的Lipschitz。