Heavy-tailed Sampling via Transformed Unadjusted Langevin Algorithm. (arXiv:2201.08349v1 [math.ST])

We analyze the oracle complexity of sampling from polynomially decaying
heavy-tailed target densities based on running the Unadjusted Langevin
Algorithm on certain transformed versions of the target density. The specific
class of closed-form transformation maps that we construct are shown to be
diffeomorphisms, and are particularly suited for developing efficient
diffusion-based samplers. We characterize the precise class of heavy-tailed
densities for which polynomial-order oracle complexities (in dimension and
inverse target accuracy) could be obtained, and provide illustrative examples.
We highlight …

algorithm arxiv math