# Langevin Monte Carlo Beyond Lipschitz Gradient Continuity

arXiv: https://arxiv.org/abs/2412.09698 · HTML: https://mlsanity.com/paper/2412.09698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 40 references that are in the map.
- First posted on arXiv 12 Dec 2024.

## Builds on (most cited first, 2 of 2)

- [On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothness](https://mlsanity.com/paper/2005.13097/) (2020)
- [Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequality](https://mlsanity.com/paper/2303.03589/) (2023)

## Abstract (arXiv)

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.