Weakly smooth Langevin Monte Carlo using p-generalized Gaussian smoothing

Langevin Monte Carlo (LMC) is an iterative process for sampling from a distribution of interests. The nonasymptotic mixing time is studied mostly in the context of smooth (gradient-Lipschitz) log-densities, a significant constraint for its deployment in many sciences including computational statistics and artificial intelligence. In the original article, [5] eliminates this restriction and establishes polynomial-time convergence assurances for a variation of LMC in the context of weakly smooth log-concave distributions. Based on their approach, we generalize the Gaussian smoothing to p-generalized Gaussian perturbation process, while maintaining the induced bias and variance bounded. We also improve their nonasymptotic dependence on the dimension and strongly convex parameters.