Langevin Monte Carlo and JKO splitting
arXiv:1802.08671
Abstract
Algorithms based on discretizing Langevin diffusion are popular tools for sampling from high-dimensional distributions. We develop novel connections between such Monte Carlo algorithms, the theory of Wasserstein gradient flow, and the operator splitting approach to solving PDEs. In particular, we show that a proximal version of the Unadjusted Langevin Algorithm corresponds to a scheme that alternates between solving the gradient flows of two specific functionals on the space of probability measures. Using this perspective, we derive some new non-asymptotic results on the convergence properties of this algorithm.
arXiv comment24 pages. Similar to arxiv:1802.08089
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- Fast and Smooth Interpolation on Wasserstein Space
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- Structured Logconcave Sampling with a Restricted Gaussian Oracle
- The Wasserstein Proximal Gradient Algorithm
- Fast Convergence of Langevin Dynamics on Manifold: Geodesics meet Log-Sobolev
- Accelerated Information Gradient flow