Optimal Scaling for the Proximal Langevin Algorithm in High Dimensions. (arXiv:2204.10793v1 [stat.CO])

The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm
that incorporates the gradient of the logarithm of the target density in its
proposal distribution. In an earlier joint work \cite{pill:stu:12}, the author
had extended the seminal work of \cite{Robe:Rose:98} and showed that in
stationarity, MALA applied to an $N$-dimensional approximation of the target
will take ${\cal O}(N^{\frac13})$ steps to explore its target measure. It was
also shown in \cite{Robe:Rose:98,pill:stu:12} that, as a consequence of the
diffusion limit, the MALA algorithm …

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