# LoCoDL: Communication-Efficient Distributed Learning with Local Training and Compression

arXiv: https://arxiv.org/abs/2403.04348 · HTML: https://mlsanity.com/paper/2403.04348/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 63 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Builds on (most cited first, 30 of 44)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [Achieving Linear Speedup with Partial Worker Participation in Non-IID Federated Learning](https://mlsanity.com/paper/2101.11203/) (2021)
- [Qsparse-local-SGD: Distributed SGD with Quantization, Sparsification, and Local Computations](https://mlsanity.com/paper/1906.02367/) (2019)
- [Federated Learning with Compression: Unified Analysis and Sharp Guarantees](https://mlsanity.com/paper/2007.01154/) (2020)
- [On Biased Compression for Distributed Learning](https://mlsanity.com/paper/2002.12410/) (2020)
- [ProxSkip: Yes! Local Gradient Steps Provably Lead to Communication Acceleration! Finally!](https://mlsanity.com/paper/2202.09357/) (2022)
- [EF21: A New, Simpler, Theoretically Better, and Practically Faster Error Feedback](https://mlsanity.com/paper/2106.05203/) (2021)
- [Distributed Learning with Compressed Gradient Differences](https://mlsanity.com/paper/1901.09269/) (2019)
- [Stochastic Controlled Averaging for Federated Learning with Communication Compression](https://mlsanity.com/paper/2308.08165/) (2023)
- [Natural Compression for Distributed Deep Learning](https://mlsanity.com/paper/1905.10988/) (2019)
- [Acceleration for Compressed Gradient Descent in Distributed and Federated Optimization](https://mlsanity.com/paper/2002.11364/) (2020)
- [A Unified Theory of SGD: Variance Reduction, Sampling, Quantization and Coordinate Descent](https://mlsanity.com/paper/1905.11261/) (2019)
- [Variance-Reduced Methods for Machine Learning](https://mlsanity.com/paper/2010.00892/) (2020)
- [MARINA: Faster Non-Convex Distributed Learning with Compression](https://mlsanity.com/paper/2102.07845/) (2021)
- [Stochastic Distributed Learning with Gradient Quantization and Variance Reduction](https://mlsanity.com/paper/1904.05115/) (2019)
- [Linearly Converging Error Compensated SGD](https://mlsanity.com/paper/2010.12292/) (2020)
- [Optimal Gradient Compression for Distributed and Federated Learning](https://mlsanity.com/paper/2010.03246/) (2020)
- [Lower Bounds and Nearly Optimal Algorithms in Distributed Learning with Communication Compression](https://mlsanity.com/paper/2206.03665/) (2022)
- [Variance Reduced ProxSkip: Algorithm, Theory and Application to Federated Learning](https://mlsanity.com/paper/2207.04338/) (2022)
- [A Double Residual Compression Algorithm for Efficient Distributed Learning](https://mlsanity.com/paper/1910.07561/) (2019)
- [RandProx: Primal-Dual Optimization Algorithms with Randomized Proximal Updates](https://mlsanity.com/paper/2207.12891/) (2022)
- [EF21-P and Friends: Improved Theoretical Communication Complexity for Distributed Optimization with Bidirectional Compression](https://mlsanity.com/paper/2209.15218/) (2022)
- [DoCoFL: Downlink Compression for Cross-Device Federated Learning](https://mlsanity.com/paper/2302.00543/) (2023)

## Built on by (most cited first, 11 of 11)

- [Unbiased and Sign Compression in Distributed Learning: Comparing Noise Resilience via SDEs](https://mlsanity.com/paper/2502.17009/) (2025)
- [Accelerated Methods with Compressed Communications for Distributed Optimization Problems under Data Similarity](https://mlsanity.com/paper/2412.16414/) (2024)
- [Convergence of Decentralized Stochastic Subgradient-based Methods for Nonsmooth Nonconvex functions](https://mlsanity.com/paper/2403.11565/) (2024)
- [Decentralized Optimization with Topology-Independent Communication](https://mlsanity.com/paper/2509.14488/) (2025)
- [BiCoLoR: Communication-Efficient Optimization with Bidirectional Compression and Local Training](https://mlsanity.com/paper/2601.12400/) (2026)
- [Gradient Compression May Hurt Generalization: A Remedy by Synthetic Data Guided Sharpness Aware Minimization](https://mlsanity.com/paper/2602.11584/) (2026)
- [FedSLoP: Memory-Efficient Federated Learning with Low-Rank Gradient Projection](https://mlsanity.com/paper/2604.24012/) (2026)
- [LOSCAR-SGD: Local SGD with Communication-Computation Overlap and Delay-Corrected Sparse Model Averaging](https://mlsanity.com/paper/2605.20866/) (2026)
- [Provable Reduction in Communication Rounds for Non-Smooth Convex Federated Learning](https://mlsanity.com/paper/2503.21627/) (2025)
- [SA-PEF: Step-Ahead Partial Error Feedback for Efficient Federated Learning](https://mlsanity.com/paper/2601.20738/) (2026)
- [LoDAdaC: a unified local training-based decentralized framework with adaptive gradients and compressed communication](https://mlsanity.com/paper/2604.09970/) (2026)

## Abstract (arXiv)

In Distributed optimization and Learning, and even more in the modern framework of federated learning, communication, which is slow and costly, is critical. We introduce LoCoDL, a communication-efficient algorithm that leverages the two popular and effective techniques of Local training, which reduces the communication frequency, and Compression, in which short bitstreams are sent instead of full-dimensional vectors of floats. LoCoDL works with a large class of unbiased compressors that includes widely-used sparsification and quantization methods. LoCoDL provably benefits from local training and compression and enjoys a doubly-accelerated communication complexity, with respect to the condition number of the functions and the model dimension, in the general heterogenous regime with strongly convex functions. This is confirmed in practice, with LoCoDL outperforming existing algorithms.