# Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising

arXiv: https://arxiv.org/abs/2208.01631 · HTML: https://mlsanity.com/paper/2208.01631/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 2 Aug 2022.

## Builds on (most cited first, 10 of 10)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Katyusha: The First Direct Acceleration of Stochastic Gradient Methods](https://mlsanity.com/paper/1603.05953/) (2016)
- [A Proximal Stochastic Gradient Method with Progressive Variance Reduction](https://mlsanity.com/paper/1403.4699/) (2014)
- [A Three-Operator Splitting Scheme and its Optimization Applications](https://mlsanity.com/paper/1504.01032/) (2015)
- [Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications](https://mlsanity.com/paper/1706.04957/) (2017)
- [Accelerated, Parallel and Proximal Coordinate Descent](https://mlsanity.com/paper/1312.5799/) (2013)
- [Mini-Batch Semi-Stochastic Gradient Descent in the Proximal Setting](https://mlsanity.com/paper/1504.04407/) (2015)
- [The Practicality of Stochastic Optimization in Imaging Inverse Problems](https://mlsanity.com/paper/1910.10100/) (2019)

## Abstract (arXiv)

In this work we propose a stochastic primal-dual three-operator splitting algorithm (TOS-SPDHG) for solving a class of convex three-composite optimization problems. Our proposed scheme is a direct three-operator splitting extension of the SPDHG algorithm [Chambolle et al. 2018]. We provide theoretical convergence analysis showing ergodic O(1/K) convergence rate, and demonstrate the effectiveness of our approach in imaging inverse problems. Moreover, we further propose TOS-SPDHG-RED and TOS-SPDHG-eRED which utilizes the regularization-by-denoising (RED) framework to leverage pretrained deep denoising networks as priors.