# Distributed Proximal Splitting Algorithms with Rates and Acceleration

arXiv: https://arxiv.org/abs/2010.00952 · HTML: https://mlsanity.com/paper/2010.00952/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2020.

## Built on by (most cited first, 7 of 7)

- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [ProxSkip: Yes! Local Gradient Steps Provably Lead to Communication Acceleration! Finally!](https://mlsanity.com/paper/2202.09357/) (2022)
- [Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient](https://mlsanity.com/paper/2301.04431/) (2023)
- [EF-BV: A Unified Theory of Error Feedback and Variance Reduction Mechanisms for Biased and Unbiased Compression in Distributed Optimization](https://mlsanity.com/paper/2205.04180/) (2022)
- [MURANA: A Generic Framework for Stochastic Variance-Reduced Optimization](https://mlsanity.com/paper/2106.03056/) (2021)
- [DADAO: Decoupled Accelerated Decentralized Asynchronous Optimization](https://mlsanity.com/paper/2208.00779/) (2022)
- [Towards a Better Theoretical Understanding of Independent Subnetwork Training](https://mlsanity.com/paper/2306.16484/) (2023)

## Abstract (arXiv)

We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the solution, as well as new accelerated versions, using varying stepsizes. In addition, we propose distributed variants of these algorithms, which can be accelerated as well. While most existing results are ergodic, our nonergodic results significantly broaden our understanding of primal-dual optimization algorithms.