Detail publikačního výsledku

Langevin Monte Carlo Beyond Lipschitz Gradient Continuity

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

Originální název

Langevin Monte Carlo Beyond Lipschitz Gradient Continuity

Anglický název

Langevin Monte Carlo Beyond Lipschitz Gradient Continuity

Druh

Stať ve sborníku v databázi WoS či Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

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

Vydáno

11.04.2025

Nakladatel

Association for the Advancement of Artificial Intelligence

Místo

Philadelphia

ISBN

978-1-57735-897-8

Kniha

Proceedings of the 39th Annual AAAI Conference on Artificial Intelligence

Strany od

15541

Strany do

15549

Strany počet

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"
}