The Query Complexity of Sampling from Strongly Log-Concave Distributions in One Dimension

Abstract

We establish the first tight lower bound of $\Omega(\log\log\kappa)$ on the query complexity of sampling from the class of strongly log-concave and log-smooth distributions with condition number $\kappa$ in one dimension. Whereas existing guarantees for MCMC-based algorithms scale polynomially in $\kappa$, we introduce a novel algorithm based on rejection sampling that closes this doubly exponential gap.

Cite

Text

Chewi et al. "The Query Complexity of Sampling from Strongly Log-Concave Distributions in One Dimension." Conference on Learning Theory, 2022.

Markdown

[Chewi et al. "The Query Complexity of Sampling from Strongly Log-Concave Distributions in One Dimension." Conference on Learning Theory, 2022.](https://mlanthology.org/colt/2022/chewi2022colt-query/)

BibTeX

@inproceedings{chewi2022colt-query,
  title     = {{The Query Complexity of Sampling from Strongly Log-Concave Distributions in One Dimension}},
  author    = {Chewi, Sinho and Gerber, Patrik R and Lu, Chen and Le Gouic, Thibaut and Rigollet, Philippe},
  booktitle = {Conference on Learning Theory},
  year      = {2022},
  pages     = {2041-2059},
  volume    = {178},
  url       = {https://mlanthology.org/colt/2022/chewi2022colt-query/}
}