  Discretization of continuous-time diffusion processes is a widely recognized
method for sampling. However, the canonical Euler-Maruyama discretization of
the Langevin diffusion process, also named as Langevin Monte Carlo (LMC),
studied mostly in the context of smooth (gradient-Lipschitz) and strongly
log-concave densities, a significant constraint for its deployment in many
sciences, including computational statistics and statistical learning. In this
paper, we establish several theoretical contributions to the literature on such
sampling methods. Particularly, we generalize the Gaussian smoothing,
approximate the gradient using p-generalized Gaussian smoothing and take
advantage of it in the context of black-box sampling. We first present a
non-strongly concave and weakly smooth black-box LMC algorithm, ideal for
practical applicability of sampling challenges in a general setting.
