# Unified analysis of SGD-type methods

arXiv: https://arxiv.org/abs/2303.16502 · HTML: https://mlsanity.com/paper/2303.16502/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 53 of its 77 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 30 of 53)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Why gradient clipping accelerates training: A theoretical justification for adaptivity](https://mlsanity.com/paper/1905.11881/) (2019)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [SARAH: A Novel Method for Machine Learning Problems Using Stochastic Recursive Gradient](https://mlsanity.com/paper/1703.00102/) (2017)
- [SGD: General Analysis and Improved Rates](https://mlsanity.com/paper/1901.09401/) (2019)
- [Minimizing Finite Sums with the Stochastic Average Gradient](https://mlsanity.com/paper/1309.2388/) (2013)
- [Handbook of Convergence Theorems for (Stochastic) Gradient Methods](https://mlsanity.com/paper/2301.11235/) (2023)
- [Better Theory for SGD in the Nonconvex World](https://mlsanity.com/paper/2002.03329/) (2020)
- [The Power of Interpolation: Understanding the Effectiveness of SGD in Modern Over-parametrized Learning](https://mlsanity.com/paper/1712.06559/) (2017)
- [QSGD: Communication-Efficient SGD via Gradient Quantization and Encoding](https://mlsanity.com/paper/1610.02132/) (2016)
- [Fast and Faster Convergence of SGD for Over-Parameterized Models and an Accelerated Perceptron](https://mlsanity.com/paper/1810.07288/) (2018)
- [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)
- [Distributed Learning with Compressed Gradient Differences](https://mlsanity.com/paper/1901.09269/) (2019)
- [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)
- [On the Convergence of SGD with Biased Gradients](https://mlsanity.com/paper/2008.00051/) (2020)
- [Unified Optimal Analysis of the (Stochastic) Gradient Method](https://mlsanity.com/paper/1907.04232/) (2019)
- [Variance-Reduced Methods for Machine Learning](https://mlsanity.com/paper/2010.00892/) (2020)
- [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)
- [Linearly Converging Error Compensated SGD](https://mlsanity.com/paper/2010.12292/) (2020)
- [Distributed learning with compressed gradients](https://mlsanity.com/paper/1806.06573/) (2018)
- [Fast Convergence of Stochastic Gradient Descent under a Strong Growth Condition](https://mlsanity.com/paper/1308.6370/) (2013)
- [A Better Alternative to Error Feedback for Communication-Efficient Distributed Learning](https://mlsanity.com/paper/2006.11077/) (2020)
- [Rethinking gradient sparsification as total error minimization](https://mlsanity.com/paper/2108.00951/) (2021)
- [Variance Reduced Stochastic Gradient Descent with Neighbors](https://mlsanity.com/paper/1506.03662/) (2015)

## Abstract (arXiv)

This note focuses on a simple approach to the unified analysis of SGD-type methods from (Gorbunov et al., 2020) for strongly convex smooth optimization problems. The similarities in the analyses of different stochastic first-order methods are discussed along with the existing extensions of the framework. The limitations of the analysis and several alternative approaches are mentioned as well.