# Faster Adaptive Decentralized Learning Algorithms

arXiv: https://arxiv.org/abs/2408.09775 · HTML: https://mlsanity.com/paper/2408.09775/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 19 Aug 2024.

## Builds on (most cited first, 27 of 27)

- [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)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Lower Bounds for Non-Convex Stochastic Optimization](https://mlsanity.com/paper/1912.02365/) (2019)
- [Momentum-Based Variance Reduction in Non-Convex SGD](https://mlsanity.com/paper/1905.10018/) (2019)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [SARAH: A Novel Method for Machine Learning Problems Using Stochastic Recursive Gradient](https://mlsanity.com/paper/1703.00102/) (2017)
- [On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization](https://mlsanity.com/paper/1808.02941/) (2018)
- [EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization](https://mlsanity.com/paper/1404.6264/) (2014)
- [On the Convergence of Stochastic Gradient Descent with Adaptive Stepsizes](https://mlsanity.com/paper/1805.08114/) (2018)
- [D2: Decentralized Training over Decentralized Data](https://mlsanity.com/paper/1803.07068/) (2018)
- [NEXT: In-Network Nonconvex Optimization](https://mlsanity.com/paper/1602.00591/) (2016)
- [Variance Reduction for Faster Non-Convex Optimization](https://mlsanity.com/paper/1603.05643/) (2016)
- [An improved convergence analysis for decentralized online stochastic non-convex optimization](https://mlsanity.com/paper/2008.04195/) (2020)
- [A Novel Convergence Analysis for Algorithms of the Adam Family](https://mlsanity.com/paper/2112.03459/) (2021)
- [SUPER-ADAM: Faster and Universal Framework of Adaptive Gradients](https://mlsanity.com/paper/2106.08208/) (2021)
- [DADAM: A Consensus-based Distributed Adaptive Gradient Method for Online Optimization](https://mlsanity.com/paper/1901.09109/) (2019)
- [ZeroSARAH: Efficient Nonconvex Finite-Sum Optimization with Zero Full Gradient Computation](https://mlsanity.com/paper/2103.01447/) (2021)
- [A Hybrid Stochastic Optimization Framework for Stochastic Composite Nonconvex Optimization](https://mlsanity.com/paper/1907.03793/) (2019)
- [Sample and Communication-Efficient Decentralized Actor-Critic Algorithms with Finite-Time Analysis](https://mlsanity.com/paper/2109.03699/) (2021)
- [A Hybrid Variance-Reduced Method for Decentralized Stochastic Non-Convex Optimization](https://mlsanity.com/paper/2102.06752/) (2021)
- [Fast decentralized non-convex finite-sum optimization with recursive variance reduction](https://mlsanity.com/paper/2008.07428/) (2020)
- [On the Convergence of Decentralized Adaptive Gradient Methods](https://mlsanity.com/paper/2109.03194/) (2021)
- [Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization](https://mlsanity.com/paper/2211.01851/) (2022)
- [D-SPIDER-SFO: A Decentralized Optimization Algorithm with Faster Convergence Rate for Nonconvex Problems](https://mlsanity.com/paper/1911.12665/) (2019)
- [GT-STORM: Taming Sample, Communication, and Memory Complexities in Decentralized Non-Convex Learning](https://mlsanity.com/paper/2105.01231/) (2021)

## Built on by (most cited first, 1 of 1)

- [A Hybrid Stochastic Gradient Tracking Method for Distributed Online Optimization Over Time-Varying Directed Networks](https://mlsanity.com/paper/2508.20645/) (2025)

## Abstract (arXiv)

Decentralized learning recently has received increasing attention in machine learning due to its advantages in implementation simplicity and system robustness, data privacy. Meanwhile, the adaptive gradient methods show superior performances in many machine learning tasks such as training neural networks. Although some works focus on studying decentralized optimization algorithms with adaptive learning rates, these adaptive decentralized algorithms still suffer from high sample complexity. To fill these gaps, we propose a class of faster adaptive decentralized algorithms (i.e., AdaMDOS and AdaMDOF) for distributed nonconvex stochastic and finite-sum optimization, respectively. Moreover, we provide a solid convergence analysis framework for our methods. In particular, we prove that our AdaMDOS obtains a near-optimal sample complexity of tildeO(ε-3) for finding an ε-stationary solution of nonconvex stochastic optimization. Meanwhile, our AdaMDOF obtains a near-optimal sample complexity of O(√nε-2) for finding an ε-stationary solution of nonconvex finite-sum optimization, where n denotes the sample size. To the best of our knowledge, our AdaMDOF algorithm is the first adaptive decentralized algorithm for nonconvex finite-sum optimization. Some experimental results demonstrate efficiency of our algorithms.