Proximal Algorithms for Accelerated Langevin Dynamics
Computational Engineering, Finance, and Science
2023-11-29 v2 Computer Vision and Pattern Recognition
Abstract
We develop a novel class of MCMC algorithms based on a stochastized Nesterov scheme. With an appropriate addition of noise, the result is a time-inhomogeneous underdamped Langevin equation, which we prove emits a specified target distribution as its invariant measure. Convergence rates to stationarity under Wasserstein-2 distance are established as well. Metropolis-adjusted and stochastic gradient versions of the proposed Langevin dynamics are also provided. Experimental illustrations show superior performance of the proposed method over typical Langevin samplers for different models in statistics and image processing including better mixing of the resulting Markov chains.
Cite
@article{arxiv.2311.14829,
title = {Proximal Algorithms for Accelerated Langevin Dynamics},
author = {Duy H. Thai and Alexander L. Young and David B. Dunson},
journal= {arXiv preprint arXiv:2311.14829},
year = {2023}
}
Comments
The technical proofs for the paper will be revised