Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithm

We propose a new method called the Metropolis-adjusted Mirror Langevin algorithm for approximate sampling from distributions whose support is a compact and convex set. This algorithm adds an accept-reject filter to the Markov chain induced by a single step of the Mirror Langevin algorithm (Zhang et al., 2020), which is a basic discretisation of the Mirror Langevin dynamics. Due to the inclusion of this filter, our method is unbiased relative to the target, while known discretisations of the Mirror Langevin …

algorithm cs.ds cs.lg filter markov math.st metropolis sampling set spaces stat.co stat.ml stat.th support