Corpus ID: 237940357

Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Sampling

@article{Wu2021MinimaxMT,
  title={Minimax Mixing Time of the Metropolis-Adjusted Langevin Algorithm for Log-Concave Sampling},
  author={Keru Wu and Scott C. Schmidler and Yuansi Chen},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.13055}
}
  • Keru Wu, S. Schmidler, Yuansi Chen
  • Published 27 September 2021
  • Computer Science, Mathematics
  • ArXiv
We study the mixing time of the Metropolis-adjusted Langevin algorithm (MALA) for sampling from a log-smooth and strongly log-concave distribution. We establish its optimal minimax mixing time under a warm start. Our main contribution is two-fold. First, for a d-dimensional log-concave density with condition number κ, we show that MALA with a warm start mixes in Õ(κ √ d) iterations up to logarithmic factors. This improves upon the previous work on the dependency of either the condition number… Expand

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