Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm

@article{Durmus2015NonasymptoticCA,
title={Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm},
author={Alain Durmus and {\'E}ric Moulines},
journal={arXiv: Statistics Theory},
year={2015}
}
• Published 17 July 2015
• Mathematics, Computer Science
• arXiv: Statistics Theory
In this paper, we study a method to sample from a target distribution $\pi$ over $\mathbb{R}^d$ having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler discretization of the overdamped Langevin stochastic differential equation associated with $\pi$. For both constant and decreasing step sizes in the Euler discretization, we obtain non-asymptotic bounds for the convergence to the target distribution $\pi$ in total…
255 Citations

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