# Accelerated Stochastic ExtraGradient: Mixing Hessian and Gradient Similarity to Reduce Communication in Distributed and Federated Learning

arXiv: https://arxiv.org/abs/2409.14280 · HTML: https://mlsanity.com/paper/2409.14280/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 22 Sep 2024.

## Builds on (most cited first, 30 of 31)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [SARAH: A Novel Method for Machine Learning Problems Using Stochastic Recursive Gradient](https://mlsanity.com/paper/1703.00102/) (2017)
- [A Survey on Distributed Machine Learning](https://mlsanity.com/paper/1912.09789/) (2019)
- [Minibatch vs Local SGD for Heterogeneous Distributed Learning](https://mlsanity.com/paper/2006.04735/) (2020)
- [On Biased Compression for Distributed Learning](https://mlsanity.com/paper/2002.12410/) (2020)
- [Katyusha: The First Direct Acceleration of Stochastic Gradient Methods](https://mlsanity.com/paper/1603.05953/) (2016)
- [Communication Efficient Distributed Optimization using an Approximate Newton-type Method](https://mlsanity.com/paper/1312.7853/) (2013)
- [PAGE: A Simple and Optimal Probabilistic Gradient Estimator for Nonconvex Optimization](https://mlsanity.com/paper/2008.10898/) (2020)
- [Local SGD: Unified Theory and New Efficient Methods](https://mlsanity.com/paper/2011.02828/) (2020)
- [A Unified Theory of SGD: Variance Reduction, Sampling, Quantization and Coordinate Descent](https://mlsanity.com/paper/1905.11261/) (2019)
- [Unified Optimal Analysis of the (Stochastic) Gradient Method](https://mlsanity.com/paper/1907.04232/) (2019)
- [Don't Jump Through Hoops and Remove Those Loops: SVRG and Katyusha are Better Without the Outer Loop](https://mlsanity.com/paper/1901.08689/) (2019)
- [Communication Complexity of Distributed Convex Learning and Optimization](https://mlsanity.com/paper/1506.01900/) (2015)
- [A Universal Catalyst for First-Order Optimization](https://mlsanity.com/paper/1506.02186/) (2015)
- [Statistically Preconditioned Accelerated Gradient Method for Distributed Optimization](https://mlsanity.com/paper/2002.10726/) (2020)
- [Decentralized Local Stochastic Extra-Gradient for Variational Inequalities](https://mlsanity.com/paper/2106.08315/) (2021)
- [On Convergence of Distributed Approximate Newton Methods: Globalization, Sharper Bounds and Beyond](https://mlsanity.com/paper/1908.02246/) (2019)
- [Faster federated optimization under second-order similarity](https://mlsanity.com/paper/2209.02257/) (2022)
- [Acceleration in Distributed Optimization under Similarity](https://mlsanity.com/paper/2110.12347/) (2021)
- [Distributed Robust Learning](https://mlsanity.com/paper/1409.5937/) (2014)
- [Differentially Private Distributed Convex Optimization via Functional Perturbation](https://mlsanity.com/paper/1512.00369/) (2015)
- [Stochastic Distributed Optimization under Average Second-order Similarity: Algorithms and Analysis](https://mlsanity.com/paper/2304.07504/) (2023)
- [A Decentralized Adaptive Momentum Method for Solving a Class of Min-Max Optimization Problems](https://mlsanity.com/paper/2106.06075/) (2021)
- [Distributed Saddle-Point Problems Under Similarity](https://mlsanity.com/paper/2107.10706/) (2021)
- [Compression and Data Similarity: Combination of Two Techniques for Communication-Efficient Solving of Distributed Variational Inequalities](https://mlsanity.com/paper/2206.09446/) (2022)
- [Similarity, Compression and Local Steps: Three Pillars of Efficient Communications for Distributed Variational Inequalities](https://mlsanity.com/paper/2302.07615/) (2023)

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

- [LionMuon: Alternating Spectral and Sign Descent for Efficient Training](https://mlsanity.com/paper/2605.19811/) (2026)
- [LionMuon: Alternating Spectral and Sign Descent for Efficient Training](https://mlsanity.com/paper/2609.35297/) (2026)

## Abstract (arXiv)

Modern realities and trends in learning require more and more generalization ability of models, which leads to an increase in both models and training sample size. It is already difficult to solve such tasks in a single device mode. This is the reason why distributed and federated learning approaches are becoming more popular every day. Distributed computing involves communication between devices, which requires solving two key problems: efficiency and privacy. One of the most well-known approaches to combat communication costs is to exploit the similarity of local data. Both Hessian similarity and homogeneous gradients have been studied in the literature, but separately. In this paper, we combine both of these assumptions in analyzing a new method that incorporates the ideas of using data similarity and clients sampling. Moreover, to address privacy concerns, we apply the technique of additional noise and analyze its impact on the convergence of the proposed method. The theory is confirmed by training on real datasets.