论文标题
在可验证的条件下MALA的几何收敛性
On the geometric convergence for MALA under verifiable conditions
论文作者
论文摘要
虽然大都会调整后的兰格文算法（MALA）是一种流行且广泛使用的马尔可夫链蒙特卡洛方法，但很少有论文得出确保其收敛性的条件。特别是，据作者的知识，仍然缺少易于验证和保证几何融合的假设。在这项工作中，我们在对目标分布的轻度假设下为MALA建立了$ V $均匀的几何融合。与以前的工作不同，我们仅考虑与目标分布相关的潜力的尾巴和平滑度条件。这些条件在MCMC文献中很普遍，在实践中易于验证。最后，我们特别注意我们得出的界限对Euler-Maruyama离散化的步长的依赖性，这与Mala的Markov Markov Kernel相对应。
While the Metropolis Adjusted Langevin Algorithm (MALA) is a popular and widely used Markov chain Monte Carlo method, very few papers derive conditions that ensure its convergence. In particular, to the authors' knowledge, assumptions that are both easy to verify and guarantee geometric convergence, are still missing. In this work, we establish $V$-uniformly geometric convergence for MALA under mild assumptions about the target distribution. Unlike previous work, we only consider tail and smoothness conditions for the potential associated with the target distribution. These conditions are quite common in the MCMC literature and are easy to verify in practice. Finally, we pay special attention to the dependence of the bounds we derive on the step size of the Euler-Maruyama discretization, which corresponds to the proposal Markov kernel of MALA.
