Publication detail
Langevin Monte Carlo Beyond Lipschitz Gradient Continuity
BENKO, M. CHLEBICKA, I. MIASOJEDOW, B. ENDAL, J.
English title
Langevin Monte Carlo Beyond Lipschitz Gradient Continuity
Type
conference paper
Language
en
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.
English 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 in English
Computational costs; Convergence rates; Improved convergence; Langevin algorithms; Langevin Monte-Carlo; Lipschitz gradients; MonteCarlo methods; Novel algorithm; Polynomial growths
Released
11.04.2025
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–to
15541–15549
Pages count
9
BIBTEX
@inproceedings{BUT198313,
author="Matej {Benko} and Iwona {Chlebicka} and Iwona {Chlebicka} and Błażej {Miasojedow} and Jørgen {Endal} and Endal {Jørgen} and Iwona {Chlebicka} and Błażej {Miasojedow} and Błażej {Miasojedow},
title="Langevin Monte Carlo Beyond Lipschitz Gradient Continuity",
booktitle="Proceedings of the 39th Annual AAAI Conference on Artificial Intelligence",
year="2025",
month="April",
pages="15541--15549",
publisher="Association for the Advancement of Artificial Intelligence",
address="Philadelphia",
isbn="978-1-57735-897-8"
}