# Taming the Interacting Particle Langevin Algorithm: The Superlinear case

arXiv: https://arxiv.org/abs/2403.19587 · HTML: https://mlsanity.com/paper/2403.19587/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 28 Mar 2024.

## Builds on (most cited first, 9 of 9)

- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1605.01559/) (2016)
- [The Tamed Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1710.05559/) (2017)
- [Particle algorithms for maximum likelihood training of latent variable models](https://mlsanity.com/paper/2204.12965/) (2022)
- [Taming neural networks with TUSLA: Non-convex learning via adaptive stochastic gradient Langevin algorithms](https://mlsanity.com/paper/2006.14514/) (2020)
- [Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimation](https://mlsanity.com/paper/2303.13429/) (2023)
- [Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networks](https://mlsanity.com/paper/2105.13937/) (2021)
- [Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function](https://mlsanity.com/paper/2107.08649/) (2021)
- [Langevin dynamics based algorithm e-THvarepsilonO POULA for stochastic optimization problems with discontinuous stochastic gradient](https://mlsanity.com/paper/2210.13193/) (2022)

## Built on by (most cited first, 3 of 3)

- [Proximal Interacting Particle Langevin Algorithms](https://mlsanity.com/paper/2406.14292/) (2024)
- [Kinetic Interacting Particle Langevin Monte Carlo](https://mlsanity.com/paper/2407.05790/) (2024)
- [Stability of Finite-Batch Particle Mean-Field Variational Inference Beyond Strong Convexity](https://mlsanity.com/paper/2608.11486/) (2026)

## Abstract (arXiv)

Recent advances in stochastic optimization have yielded the interacting particle Langevin algorithm (IPLA), which leverages the notion of interacting particle systems (IPS) to efficiently sample from approximate posterior densities. This becomes particularly crucial in relation to the framework of Expectation-Maximization (EM), where the E-step is computationally challenging or even intractable. Although prior research has focused on scenarios involving convex cases with gradients of log densities that grow at most linearly, our work extends this framework to include polynomial growth. Taming techniques are employed to produce an explicit discretization scheme that yields a new class of stable, under such non-linearities, algorithms which are called tamed interacting particle Langevin algorithms (tIPLA). We obtain non-asymptotic convergence error estimates in Wasserstein-2 distance for the new class under the best known rate.