# Error Compensated Loopless SVRG, Quartz, and SDCA for Distributed Optimization

arXiv: https://arxiv.org/abs/2109.10049 · HTML: https://mlsanity.com/paper/2109.10049/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2021.

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

- [Basis Matters: Better Communication-Efficient Second Order Methods for Federated Learning](https://mlsanity.com/paper/2111.01847/) (2021)
- [EControl: Fast Distributed Optimization with Compression and Error Control](https://mlsanity.com/paper/2311.05645/) (2023)
- [Towards a Better Theoretical Understanding of Independent Subnetwork Training](https://mlsanity.com/paper/2306.16484/) (2023)
- [Personalized Federated Learning with Multiple Known Clusters](https://mlsanity.com/paper/2204.13619/) (2022)

## Abstract (arXiv)

The communication of gradients is a key bottleneck in distributed training of large scale machine learning models. In order to reduce the communication cost, gradient compression (e.g., sparsification and quantization) and error compensation techniques are often used. In this paper, we propose and study three new efficient methods in this space: error compensated loopless SVRG method (EC-LSVRG), error compensated Quartz (EC-Quartz), and error compensated SDCA (EC-SDCA). Our method is capable of working with any contraction compressor (e.g., TopK compressor), and we perform analysis for convex optimization problems in the composite case and smooth case for EC-LSVRG. We prove linear convergence rates for both cases and show that in the smooth case the rate has a better dependence on the parameter associated with the contraction compressor. Further, we show that in the smooth case, and under some certain conditions, error compensated loopless SVRG has the same convergence rate as the vanilla loopless SVRG method. Then we show that the convergence rates of EC-Quartz and EC-SDCA in the composite case are as good as EC-LSVRG in the smooth case. Finally, numerical experiments are presented to illustrate the efficiency of our methods.