We consider a recently proposed class of MCMC methods which uses proximity maps instead of gradients to build proposal mechanisms which can be employed for both differentiable and non-differentiable targets. These methods have been shown to be stable for a wide class of targets, making them a valuable alternative to Metropolis-adjusted Langevin algorithms (MALA); and have found wide application in imaging contexts. The wider stability properties are obtained by building the Moreau-Yoshida envelope for the target of interest, which depends on a parameter $\lambda$. In this work, we investigate the optimal scaling problem for this class of algorithms, which encompasses MALA, and provide practical guidelines for the implementation of these methods.

翻译：本文研究了一类最近提出的MCMC方法，该方法使用近端映射代替梯度来构建提议机制，可适用于可微和非可微目标分布。这类方法已被证明对广泛的目标分布具有稳定性，成为Metropolis调整Langevin算法（MALA）的重要替代方案，并在图像处理领域得到广泛应用。其更广泛的稳定性是通过构建依赖于参数$\lambda$的目标分布的Moreau-Yoshida包络实现的。在本工作中，我们研究了包含MALA在内的这类算法的最优缩放问题，并为这些方法的实现提供了实用指南。