# On Biased Compression for Distributed Learning

arXiv: https://arxiv.org/abs/2002.12410 · HTML: https://mlsanity.com/paper/2002.12410/

## Key facts

- Cited by 140 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2020.

## Built on by (most cited first, 30 of 140)

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- [EDEN: Communication-Efficient and Robust Distributed Mean Estimation for Federated Learning](https://mlsanity.com/paper/2108.08842/) (2021)
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- [Moshpit SGD: Communication-Efficient Decentralized Training on Heterogeneous Unreliable Devices](https://mlsanity.com/paper/2103.03239/) (2021)
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- [DoCoFL: Downlink Compression for Cross-Device Federated Learning](https://mlsanity.com/paper/2302.00543/) (2023)
- [3PC: Three Point Compressors for Communication-Efficient Distributed Training and a Better Theory for Lazy Aggregation](https://mlsanity.com/paper/2202.00998/) (2022)
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- [CANITA: Faster Rates for Distributed Convex Optimization with Communication Compression](https://mlsanity.com/paper/2107.09461/) (2021)
- [Smoothness Matrices Beat Smoothness Constants: Better Communication Compression Techniques for Distributed Optimization](https://mlsanity.com/paper/2102.07245/) (2021)
- [Preserved central model for faster bidirectional compression in distributed settings](https://mlsanity.com/paper/2102.12528/) (2021)
- [On Distributed Adaptive Optimization with Gradient Compression](https://mlsanity.com/paper/2205.05632/) (2022)
- [Federated Optimization Algorithms with Random Reshuffling and Gradient Compression](https://mlsanity.com/paper/2206.07021/) (2022)
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- [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)
- [DASHA: Distributed Nonconvex Optimization with Communication Compression, Optimal Oracle Complexity, and No Client Synchronization](https://mlsanity.com/paper/2202.01268/) (2022)

## Abstract (arXiv)

In the last few years, various communication compression techniques have emerged as an indispensable tool helping to alleviate the communication bottleneck in distributed learning. However, despite the fact biased compressors often show superior performance in practice when compared to the much more studied and understood unbiased compressors, very little is known about them. In this work we study three classes of biased compression operators, two of which are new, and their performance when applied to (stochastic) gradient descent and distributed (stochastic) gradient descent. We show for the first time that biased compressors can lead to linear convergence rates both in the single node and distributed settings. We prove that distributed compressed SGD method, employed with error feedback mechanism, enjoys the ergodic rate Oleft( δ L exp left[-fracμ Kδ Lright] + frac(C + δ D)Kμright), where δ≥ 1 is a compression parameter which grows when more compression is applied, L and μ are the smoothness and strong convexity constants, C captures stochastic gradient noise (C=0 if full gradients are computed on each node) and D captures the variance of the gradients at the optimum (D=0 for over-parameterized models). Further, via a theoretical study of several synthetic and empirical distributions of communicated gradients, we shed light on why and by how much biased compressors outperform their unbiased variants. Finally, we propose several new biased compressors with promising theoretical guarantees and practical performance.