Langevin Monte Carlo Beyond Lipschitz Gradient Continuity

Matej Benko, Iwona Chlebicka, Jørgen Endal, Błażej Miasojedow
12/12/2024
stat.MLcs.LG

No official code found. Best implementation: 192459/lmc-beyond-lipschitz-gradient-continuity (0 stars, MIT, last commit 2026-03-25).

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.

View on arXivView PDF

Code Implementations(1)

192459/lmc-beyond-lipschitz-gradient-continuityCommunity100%
MIT

Codes of simulations suuporting our theoretical results in the paper of Matej Benko, Iwona Chlebicka, Jørgen Endal, Bła˙zej Miasojedow: Langevin Monte Carlo Beyond Lipschitz Gradient Continuity

00Python, Jupyter NotebookDec 12, 20246 months agoMIT

Similar Papers

High-Order Langevin Monte Carlo Algorithms

83% match2025

Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisited

82% match2023

Stochastic Langevin Monte Carlo for (weakly) log-concave posterior distributions

80% match2023

Constrained Sampling with Primal-Dual Langevin Monte Carlo

80% match1 repo12024

Langevin Monte-Carlo Provably Learns Depth Two Neural Nets at Any Size and Data

79% match2025

Subspace Langevin Monte Carlo

79% match2024

Cite this paper

@article{benko2024langevin,
  title  = {Langevin Monte Carlo Beyond Lipschitz Gradient Continuity},
  author = {Matej Benko and Iwona Chlebicka and Jørgen Endal and Błażej Miasojedow},
  year   = {2024},
  eprint = {2412.09698},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2412.09698v1}
}

Add a badge to your README

Shows whether official code is linked for this paper.

Code of Paper badge
[![Code of Paper](https://codeofpaper.com/badge/2412.09698.svg)](https://codeofpaper.com/paper/2412.09698)

Discussion