# MARINA: Faster Non-Convex Distributed Learning with Compression

arXiv: https://arxiv.org/abs/2102.07845 · HTML: https://mlsanity.com/paper/2102.07845/

## Key facts

- Cited by 78 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 46 references that are in the map.
- First posted on arXiv 15 Feb 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Large Batch Optimization for Deep Learning: Training BERT in 76 minutes](https://mlsanity.com/paper/1904.00962/) (2019)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Error Feedback Fixes SignSGD and other Gradient Compression Schemes](https://mlsanity.com/paper/1901.09847/) (2019)
- [Lower Bounds for Non-Convex Stochastic Optimization](https://mlsanity.com/paper/1912.02365/) (2019)
- [SPIDER: Near-Optimal Non-Convex Optimization via Stochastic Path Integrated Differential Estimator](https://mlsanity.com/paper/1807.01695/) (2018)
- [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)
- [Distributed Mean Estimation with Limited Communication](https://mlsanity.com/paper/1611.00429/) (2016)
- [Lower Bounds for Finding Stationary Points I](https://mlsanity.com/paper/1710.11606/) (2017)
- [PAGE: A Simple and Optimal Probabilistic Gradient Estimator for Nonconvex Optimization](https://mlsanity.com/paper/2008.10898/) (2020)
- [Decentralized Deep Learning with Arbitrary Communication Compression](https://mlsanity.com/paper/1907.09356/) (2019)
- [Natural Compression for Distributed Deep Learning](https://mlsanity.com/paper/1905.10988/) (2019)
- [Optimization for deep learning: theory and algorithms](https://mlsanity.com/paper/1912.08957/) (2019)
- [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)
- [Uncertainty Principle for Communication Compression in Distributed and Federated Learning and the Search for an Optimal Compressor](https://mlsanity.com/paper/2002.08958/) (2020)
- [Error Compensated Distributed SGD Can Be Accelerated](https://mlsanity.com/paper/2010.00091/) (2020)
- [Dropping Convexity for Faster Semi-definite Optimization](https://mlsanity.com/paper/1509.03917/) (2015)
- [Randomized Distributed Mean Estimation: Accuracy vs Communication](https://mlsanity.com/paper/1611.07555/) (2016)
- [Recent Theoretical Advances in Non-Convex Optimization](https://mlsanity.com/paper/2012.06188/) (2020)
- [A Unified Analysis of Stochastic Gradient Methods for Nonconvex Federated Optimization](https://mlsanity.com/paper/2006.07013/) (2020)
- [Communication-Efficient Local Decentralized SGD Methods](https://mlsanity.com/paper/1910.09126/) (2019)
- [Adaptivity of Stochastic Gradient Methods for Nonconvex Optimization](https://mlsanity.com/paper/2002.05359/) (2020)

## Built on by (most cited first, 30 of 78)

- [EF21: A New, Simpler, Theoretically Better, and Practically Faster Error Feedback](https://mlsanity.com/paper/2106.05203/) (2021)
- [Fast Federated Learning in the Presence of Arbitrary Device Unavailability](https://mlsanity.com/paper/2106.04159/) (2021)
- [EDEN: Communication-Efficient and Robust Distributed Mean Estimation for Federated Learning](https://mlsanity.com/paper/2108.08842/) (2021)
- [FedNL: Making Newton-Type Methods Applicable to Federated Learning](https://mlsanity.com/paper/2106.02969/) (2021)
- [BEER: Fast O(1/T) Rate for Decentralized Nonconvex Optimization with Communication Compression](https://mlsanity.com/paper/2201.13320/) (2022)
- [Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methods](https://mlsanity.com/paper/2202.07262/) (2022)
- [Moshpit SGD: Communication-Efficient Decentralized Training on Heterogeneous Unreliable Devices](https://mlsanity.com/paper/2103.03239/) (2021)
- [SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression](https://mlsanity.com/paper/2206.09888/) (2022)
- [Lower Bounds and Nearly Optimal Algorithms in Distributed Learning with Communication Compression](https://mlsanity.com/paper/2206.03665/) (2022)
- [Momentum Provably Improves Error Feedback!](https://mlsanity.com/paper/2305.15155/) (2023)
- [Fine-tuning Language Models over Slow Networks using Activation Compression with Guarantees](https://mlsanity.com/paper/2206.01299/) (2022)
- [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)
- [CANITA: Faster Rates for Distributed Convex Optimization with Communication Compression](https://mlsanity.com/paper/2107.09461/) (2021)
- [Server-Side Stepsizes and Sampling Without Replacement Provably Help in Federated Optimization](https://mlsanity.com/paper/2201.11066/) (2022)
- [FedShuffle: Recipes for Better Use of Local Work in Federated Learning](https://mlsanity.com/paper/2204.13169/) (2022)
- [FedPAGE: A Fast Local Stochastic Gradient Method for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2108.04755/) (2021)
- [Communication Acceleration of Local Gradient Methods via an Accelerated Primal-Dual Algorithm with Inexact Prox](https://mlsanity.com/paper/2207.03957/) (2022)
- [Privacy-Aware Compression for Federated Data Analysis](https://mlsanity.com/paper/2203.08134/) (2022)
- [DASHA: Distributed Nonconvex Optimization with Communication Compression, Optimal Oracle Complexity, and No Client Synchronization](https://mlsanity.com/paper/2202.01268/) (2022)
- [Distributed Methods with Compressed Communication for Solving Variational Inequalities, with Theoretical Guarantees](https://mlsanity.com/paper/2110.03313/) (2021)
- [Faster Rates for Compressed Federated Learning with Client-Variance Reduction](https://mlsanity.com/paper/2112.13097/) (2021)
- [Anchor Sampling for Federated Learning with Partial Client Participation](https://mlsanity.com/paper/2206.05891/) (2022)
- [Coresets for Vertical Federated Learning: Regularized Linear Regression and K-Means Clustering](https://mlsanity.com/paper/2210.14664/) (2022)
- [Secure Distributed Training at Scale](https://mlsanity.com/paper/2106.11257/) (2021)
- [Lottery Aware Sparsity Hunting: Enabling Federated Learning on Resource-Limited Edge](https://mlsanity.com/paper/2208.13092/) (2022)
- [Federated Learning with Flexible Control](https://mlsanity.com/paper/2212.08496/) (2022)
- [Communication Compression for Byzantine Robust Learning: New Efficient Algorithms and Improved Rates](https://mlsanity.com/paper/2310.09804/) (2023)
- [Distributed Newton-Type Methods with Communication Compression and Bernoulli Aggregation](https://mlsanity.com/paper/2206.03588/) (2022)
- [Lower Bounds and Accelerated Algorithms in Distributed Stochastic Optimization with Communication Compression](https://mlsanity.com/paper/2305.07612/) (2023)

## Abstract (arXiv)

We develop and analyze MARINA: a new communication efficient method for non-convex distributed learning over heterogeneous datasets. MARINA employs a novel communication compression strategy based on the compression of gradient differences that is reminiscent of but different from the strategy employed in the DIANA method of Mishchenko et al. (2019). Unlike virtually all competing distributed first-order methods, including DIANA, ours is based on a carefully designed biased gradient estimator, which is the key to its superior theoretical and practical performance. The communication complexity bounds we prove for MARINA are evidently better than those of all previous first-order methods. Further, we develop and analyze two variants of MARINA: VR-MARINA and PP-MARINA. The first method is designed for the case when the local loss functions owned by clients are either of a finite sum or of an expectation form, and the second method allows for a partial participation of clients -- a feature important in federated learning. All our methods are superior to previous state-of-the-art methods in terms of oracle/communication complexity. Finally, we provide a convergence analysis of all methods for problems satisfying the Polyak-Lojasiewicz condition.