# Communication Compression for Decentralized Learning with Operator Splitting Methods

arXiv: https://arxiv.org/abs/2205.03779 · HTML: https://mlsanity.com/paper/2205.03779/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 51 references that are in the map.
- First posted on arXiv 8 May 2022.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication](https://mlsanity.com/paper/1902.00340/) (2019)
- [Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs](https://mlsanity.com/paper/1607.03218/) (2016)
- [D2: Decentralized Training over Decentralized Data](https://mlsanity.com/paper/1803.07068/) (2018)
- [Decentralized Deep Learning with Arbitrary Communication Compression](https://mlsanity.com/paper/1907.09356/) (2019)
- [NEXT: In-Network Nonconvex Optimization](https://mlsanity.com/paper/1602.00591/) (2016)
- [Communication Compression for Decentralized Training](https://mlsanity.com/paper/1803.06443/) (2018)
- [Decentralized Federated Learning: Balancing Communication and Computing Costs](https://mlsanity.com/paper/2107.12048/) (2021)
- [A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates](https://mlsanity.com/paper/1704.07807/) (2017)
- [Exact Diffusion for Distributed Optimization and Learning --- Part I: Algorithm Development](https://mlsanity.com/paper/1702.05122/) (2017)
- [A Better Alternative to Error Feedback for Communication-Efficient Distributed Learning](https://mlsanity.com/paper/2006.11077/) (2020)
- [A Linearly Convergent Algorithm for Decentralized Optimization: Sending Less Bits for Free!](https://mlsanity.com/paper/2011.01697/) (2020)
- [BEER: Fast O(1/T) Rate for Decentralized Nonconvex Optimization with Communication Compression](https://mlsanity.com/paper/2201.13320/) (2022)
- [RelaySum for Decentralized Deep Learning on Heterogeneous Data](https://mlsanity.com/paper/2110.04175/) (2021)
- [PowerGossip: Practical Low-Rank Communication Compression in Decentralized Deep Learning](https://mlsanity.com/paper/2008.01425/) (2020)
- [Variance-Reduced Decentralized Stochastic Optimization with Accelerated Convergence](https://mlsanity.com/paper/1912.04230/) (2019)
- [Moniqua: Modulo Quantized Communication in Decentralized SGD](https://mlsanity.com/paper/2002.11787/) (2020)
- [Linear Convergent Decentralized Optimization with Compression](https://mlsanity.com/paper/2007.00232/) (2020)
- [Distributed Optimization Using the Primal-Dual Method of Multipliers](https://mlsanity.com/paper/1702.00841/) (2017)

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

- [Momentum Tracking: Momentum Acceleration for Decentralized Deep Learning on Heterogeneous Data](https://mlsanity.com/paper/2209.15505/) (2022)
- [UCCL-Zip: Lossless Compression Supercharged GPU Communication](https://mlsanity.com/paper/2604.17172/) (2026)

## Abstract (arXiv)

In decentralized learning, operator splitting methods using a primal-dual formulation (e.g., the Edge-Consensus Learning (ECL)) has been shown to be robust to heterogeneous data and has attracted significant attention in recent years. However, in the ECL, a node needs to exchange dual variables with its neighbors. These exchanges incur significant communication costs. For the Gossip-based algorithms, many compression methods have been proposed, but these Gossip-based algorithm do not perform well when the data distribution held by each node is statistically heterogeneous. In this work, we propose the novel framework of the compression methods for the ECL, called the Communication Compressed ECL (C-ECL). Specifically, we reformulate the update formulas of the ECL, and propose to compress the update values of the dual variables. We demonstrate experimentally that the C-ECL can achieve a nearly equivalent performance with fewer parameter exchanges than the ECL. Moreover, we demonstrate that the C-ECL is more robust to heterogeneous data than the Gossip-based algorithms.