# A Unified Momentum-based Paradigm of Decentralized SGD for Non-Convex Models and Heterogeneous Data

arXiv: https://arxiv.org/abs/2303.00179 · HTML: https://mlsanity.com/paper/2303.00179/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 47 references that are in the map.
- First posted on arXiv 1 Mar 2023.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [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)
- [The Non-IID Data Quagmire of Decentralized Machine Learning](https://mlsanity.com/paper/1910.00189/) (2019)
- [SPIDER: Near-Optimal Non-Convex Optimization via Stochastic Path Integrated Differential Estimator](https://mlsanity.com/paper/1807.01695/) (2018)
- [Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication](https://mlsanity.com/paper/1902.00340/) (2019)
- [On the Linear Speedup Analysis of Communication Efficient Momentum SGD for Distributed Non-Convex Optimization](https://mlsanity.com/paper/1905.03817/) (2019)
- [Generalized Federated Learning via Sharpness Aware Minimization](https://mlsanity.com/paper/2206.02618/) (2022)
- [Momentum Improves Normalized SGD](https://mlsanity.com/paper/2002.03305/) (2020)
- [SlowMo: Improving Communication-Efficient Distributed SGD with Slow Momentum](https://mlsanity.com/paper/1910.00643/) (2019)
- [NEXT: In-Network Nonconvex Optimization](https://mlsanity.com/paper/1602.00591/) (2016)
- [Quasi-Global Momentum: Accelerating Decentralized Deep Learning on Heterogeneous Data](https://mlsanity.com/paper/2102.04761/) (2021)
- [An Improved Analysis of Gradient Tracking for Decentralized Machine Learning](https://mlsanity.com/paper/2202.03836/) (2022)
- [Federated Learning on Heterogeneous and Long-Tailed Data via Classifier Re-Training with Federated Features](https://mlsanity.com/paper/2204.13399/) (2022)
- [Global convergence of the Heavy-ball method for convex optimization](https://mlsanity.com/paper/1412.7457/) (2014)
- [A Unified Analysis of Stochastic Momentum Methods for Deep Learning](https://mlsanity.com/paper/1808.10396/) (2018)
- [An improved convergence analysis for decentralized online stochastic non-convex optimization](https://mlsanity.com/paper/2008.04195/) (2020)
- [Cross-Gradient Aggregation for Decentralized Learning from Non-IID data](https://mlsanity.com/paper/2103.02051/) (2021)
- [Convergence of a Stochastic Gradient Method with Momentum for Non-Smooth Non-Convex Optimization](https://mlsanity.com/paper/2002.05466/) (2020)
- [FedDUAP: Federated Learning with Dynamic Update and Adaptive Pruning Using Shared Data on the Server](https://mlsanity.com/paper/2204.11536/) (2022)
- [A Hybrid Variance-Reduced Method for Decentralized Stochastic Non-Convex Optimization](https://mlsanity.com/paper/2102.06752/) (2021)
- [Shielding Federated Learning: Robust Aggregation with Adaptive Client Selection](https://mlsanity.com/paper/2204.13256/) (2022)
- [Minibatch and Momentum Model-based Methods for Stochastic Weakly Convex Optimization](https://mlsanity.com/paper/2106.03034/) (2021)
- [Riemannian stochastic recursive momentum method for non-convex optimization](https://mlsanity.com/paper/2008.04555/) (2020)
- [The Role of Momentum Parameters in the Optimal Convergence of Adaptive Polyak's Heavy-ball Methods](https://mlsanity.com/paper/2102.07314/) (2021)

## Abstract (arXiv)

Emerging distributed applications recently boosted the development of decentralized machine learning, especially in IoT and edge computing fields. In real-world scenarios, the common problems of non-convexity and data heterogeneity result in inefficiency, performance degradation, and development stagnation. The bulk of studies concentrates on one of the issues mentioned above without having a more general framework that has been proven optimal. To this end, we propose a unified paradigm called UMP, which comprises two algorithms, D-SUM and GT-DSUM, based on the momentum technique with decentralized stochastic gradient descent(SGD). The former provides a convergence guarantee for general non-convex objectives. At the same time, the latter is extended by introducing gradient tracking, which estimates the global optimization direction to mitigate data heterogeneity(i.e., distribution drift). We can cover most momentum-based variants based on the classical heavy ball or Nesterov's acceleration with different parameters in UMP. In theory, we rigorously provide the convergence analysis of these two approaches for non-convex objectives and conduct extensive experiments, demonstrating a significant improvement in model accuracy by up to 57.6% compared to other methods in practice.