# Exponential ergodicity of mirror-Langevin diffusions

@article{Chewi2020ExponentialEO, title={Exponential ergodicity of mirror-Langevin diffusions}, author={Sinho Chewi and Thibaut Le Gouic and Chen Lu and Tyler Maunu and Philippe Rigollet and Austin Stromme}, journal={ArXiv}, year={2020}, volume={abs/2005.09669} }

Motivated by the problem of sampling from ill-conditioned log-concave distributions, we give a clean non-asymptotic convergence analysis of mirror-Langevin diffusions as introduced in Zhang et al. (2020). As a special case of this framework, we propose a class of diffusions called Newton-Langevin diffusions and prove that they converge to stationarity exponentially fast with a rate which not only is dimension-free, but also has no dependence on the target distribution. We give an application of…

## 21 Citations

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