Publication detail

Langevin Monte Carlo Beyond Lipschitz Gradient Continuity

BENKO, M. CHLEBICKA, I. MIASOJEDOW, B. ENDAL, J.

Original Title

Langevin Monte Carlo Beyond Lipschitz Gradient Continuity

Type

conference paper

Language

English

Original Abstract

We present a significant advancement in the field of Langevin Monte Carlo (LMC) methods by introducing the Inexact Proximal Langevin Algorithm (IPLA). This novel algorithm broadens the scope of problems that LMC can effectively address while maintaining controlled computational costs. IPLA extends LMC's applicability to potentials that are convex, strongly convex in the tails, and exhibit polynomial growth, beyond the conventional L-smoothness assumption. Moreover, we extend LMC's applicability to super-quadratic potentials and offer improved convergence rates over existing algorithms. Additionally, we provide bounds on all moments of the Markov chain generated by IPLA, enhancing its analytical robustness.

Keywords

Computational costs; Convergence rates; Improved convergence; Langevin algorithms; Langevin Monte-Carlo; Lipschitz gradients; MonteCarlo methods; Novel algorithm; Polynomial growths

Authors

BENKO, M.; CHLEBICKA, I.; MIASOJEDOW, B.; ENDAL, J.

Released

11. 4. 2025

Publisher

Association for the Advancement of Artificial Intelligence

Location

Philadelphia

ISBN

978-1-57735-897-8

Book

Proceedings of the 39th Annual AAAI Conference on Artificial Intelligence

Pages from

15541

Pages to

15549

Pages count

9

URL

https://ojs.aaai.org/index.php/AAAI/article/view/33706

BibTex

@inproceedings{BUT198313,
  author="Matej {Benko} and Iwona {Chlebicka} and Endal {Jørgen} and Błażej {Miasojedow}",
  title="Langevin Monte Carlo Beyond Lipschitz Gradient Continuity",
  booktitle="Proceedings of the 39th Annual AAAI Conference on Artificial Intelligence",
  year="2025",
  pages="15541--15549",
  publisher="Association for the Advancement of Artificial Intelligence",
  address="Philadelphia",
  doi="10.1609/aaai.v39i15.33706",
  isbn="978-1-57735-897-8",
  url="https://ojs.aaai.org/index.php/AAAI/article/view/33706"
}

Responsibility: Ing. Marek Strakoš