Spectral Gap of Replica Exchange Langevin Diffusion on Mixture Distributions

Understand

Langevin diffusion (LD) is one of the main workhorses for sampling problems.

• However, its convergence rate can be significantly reduced if the target distribution is a mixture of multiple densities, especially when each component concentrates around a different mode.
• Replica exchange Langevin diffusion (ReLD) is a sampling method that can circumvent this issue.
• In particular, ReLD adds another LD sampling a high-temperature version of the target density, and exchange the locations of two LDs according to a Metropolis-Hasting type of law.