# Proximal-Proximal-Gradient Method

arXiv: https://arxiv.org/abs/1708.06908 · HTML: https://mlsanity.com/paper/1708.06908/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2017.

## Built on by (most cited first, 2 of 2)

- [Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks](https://mlsanity.com/paper/2404.18769/) (2024)
- [TenIPS: Inverse Propensity Sampling for Tensor Completion](https://mlsanity.com/paper/2101.00323/) (2021)

## Abstract (arXiv)

In this paper, we present the proximal-proximal-gradient method (PPG), a novel optimization method that is simple to implement and simple to parallelize. PPG generalizes the proximal-gradient method and ADMM and is applicable to minimization problems written as a sum of many differentiable and many non-differentiable convex functions. The non-differentiable functions can be coupled. We furthermore present a related stochastic variation, which we call stochastic PPG (S-PPG). S-PPG can be interpreted as a generalization of Finito and MISO over to the sum of many coupled non-differentiable convex functions. We present many applications that can benefit from PPG and S-PPG and prove convergence for both methods. A key strength of PPG and S-PPG is, compared to existing methods, its ability to directly handle a large sum of non-differentiable non-separable functions with a constant stepsize independent of the number of functions. Such non-diminishing stepsizes allows them to be fast.