# On perturbed proximal gradient algorithms

arXiv: https://arxiv.org/abs/1402.2365 · HTML: https://mlsanity.com/paper/1402.2365/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2014.

## Built on by (most cited first, 4 of 4)

- [Kinetic Interacting Particle Langevin Monte Carlo](https://mlsanity.com/paper/2407.05790/) (2024)
- [Online Estimation and Optimization of Utility-Based Shortfall Risk](https://mlsanity.com/paper/2111.08805/) (2021)
- [Sharper Bounds for Proximal Gradient Algorithms with Errors](https://mlsanity.com/paper/2203.02204/) (2022)
- [A High-order Tuner for Accelerated Learning and Control](https://mlsanity.com/paper/2103.12868/) (2021)

## Abstract (arXiv)

We study a version of the proximal gradient algorithm for which the gradient is intractable and is approximated by Monte Carlo methods (and in particular Markov Chain Monte Carlo). We derive conditions on the step size and the Monte Carlo batch size under which convergence is guaranteed: both increasing batch size and constant batch size are considered. We also derive non-asymptotic bounds for an averaged version. Our results cover both the cases of biased and unbiased Monte Carlo approximation. To support our findings, we discuss the inference of a sparse generalized linear model with random effect and the problem of learning the edge structure and parameters of sparse undirected graphical models.