Penalized Overdamped and Underdamped Langevin Monte Carlo Algorithms for Constrained Sampling

arXiv:2212.00570v2 Announce Type: replace-cross
Abstract: We consider the constrained sampling problem where the goal is to sample from a target distribution $\pi(x)\propto e^{-f(x)}$ when $x$ is constrained to lie on a convex body $\mathcal{C}$. Motivated by penalty methods from continuous optimization, we propose penalized Langevin Dynamics (PLD) and penalized underdamped Langevin Monte Carlo (PULMC) methods that convert the constrained sampling problem into an unconstrained sampling problem by introducing a penalty function for constraint violations. When $f$ is smooth and gradients …

abstract algorithms arxiv continuous cs.lg distribution dynamics optimization sample sampling stat.co stat.ml type