On Mixing Times of Metropolized Algorithm With Optimization Step (MAO) : A New Framework
This provides a new framework for sampling from challenging distributions, which is incremental but offers theoretical guarantees where existing methods like MALA lack them.
The paper tackles sampling from thin-tailed distributions in high dimensions by proposing the Metropolized Algorithm With Optimization Step (MAO), which addresses cases where MALA fails, and derives upper bounds on its mixing time, supported by simulations on multiple targets.
In this paper, we consider sampling from a class of distributions with thin tails supported on $\mathbb{R}^d$ and make two primary contributions. First, we propose a new Metropolized Algorithm With Optimization Step (MAO), which is well suited for such targets. Our algorithm is capable of sampling from distributions where the Metropolis-adjusted Langevin algorithm (MALA) is not converging or lacking in theoretical guarantees. Second, we derive upper bounds on the mixing time of MAO. Our results are supported by simulations on multiple target distributions.