# Reflected Anchored Langevin Algorithms

arXiv: https://arxiv.org/abs/2610.09522 · HTML: https://mlsanity.com/paper/2610.09522/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 54 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 6 of 6)

- [Generalized EXTRA stochastic gradient Langevin dynamics](https://mlsanity.com/paper/2412.01993/) (2024)
- [Non-Reversible Langevin Algorithms for Constrained Sampling](https://mlsanity.com/paper/2501.11743/) (2025)
- [DIGing--SGLD: Decentralized and Scalable Langevin Sampling over Time--Varying Networks](https://mlsanity.com/paper/2511.12836/) (2025)
- [Regime-Switching Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2509.00941/) (2025)
- [Anchored Langevin Algorithms](https://mlsanity.com/paper/2509.19455/) (2025)
- [Decentralized Proximal Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2605.00723/) (2026)

## Built on by (most cited first, 1 of 1)

- [Accelerating Non-Smooth and Heavy-Tailed Sampling](https://mlsanity.com/paper/2610.11139/) (2026)

## Abstract (arXiv)

First order Langevin algorithms for constrained sampling in machine learning, such as projected Langevin Monte Carlo which are based on discretizations of reflected Langevin dynamics, require differentiable log densities that limits their applicability. This paper introduces reflected anchored Langevin dynamics (RALD), a reflected diffusion that converges to non-differentiable targets on constrained domains. The method uses a smooth anchored reference potential and multiplies the drift and noise covariance of its reflected Langevin dynamics by the same state dependent scaling factor. Its Euler-Maruyama discretization with projection gives reflected anchored Langevin Monte Carlo (RALMC) algorithm. We prove explicit convergence bounds and iteration complexity for RALMC in the 2-Wasserstein distance to the target distribution. Numerical experiments are provided to illustrate the theoretical predictions and the empirical performance of the method.