# Effectiveness of Distributed Gradient Descent with Local Steps for Overparameterized Models

arXiv: https://arxiv.org/abs/2412.07971 · HTML: https://mlsanity.com/paper/2412.07971/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 62 references that are in the map.
- First posted on arXiv 10 Dec 2024.

## Builds on (most cited first, 30 of 43)

- [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)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Do Better ImageNet Models Transfer Better?](https://mlsanity.com/paper/1805.08974/) (2018)
- [DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition](https://mlsanity.com/paper/1310.1531/) (2013)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Horovod: fast and easy distributed deep learning in TensorFlow](https://mlsanity.com/paper/1802.05799/) (2018)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss](https://mlsanity.com/paper/2002.04486/) (2020)
- [Characterizing Implicit Bias in Terms of Optimization Geometry](https://mlsanity.com/paper/1802.08246/) (2018)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [SMART: Robust and Efficient Fine-Tuning for Pre-trained Natural Language Models through Principled Regularized Optimization](https://mlsanity.com/paper/1911.03437/) (2019)
- [Implicit Bias of Gradient Descent on Linear Convolutional Networks](https://mlsanity.com/paper/1806.00468/) (2018)
- [Don't Use Large Mini-Batches, Use Local SGD](https://mlsanity.com/paper/1808.07217/) (2018)
- [Gradient descent aligns the layers of deep linear networks](https://mlsanity.com/paper/1810.02032/) (2018)
- [FedBE: Making Bayesian Model Ensemble Applicable to Federated Learning](https://mlsanity.com/paper/2009.01974/) (2020)
- [Is Local SGD Better than Minibatch SGD?](https://mlsanity.com/paper/2002.07839/) (2020)
- [DiLoCo: Distributed Low-Communication Training of Language Models](https://mlsanity.com/paper/2311.08105/) (2023)
- [Stochastic Controlled Averaging for Federated Learning with Communication Compression](https://mlsanity.com/paper/2308.08165/) (2023)
- [How catastrophic can catastrophic forgetting be in linear regression?](https://mlsanity.com/paper/2205.09588/) (2022)
- [On Large-Cohort Training for Federated Learning](https://mlsanity.com/paper/2106.07820/) (2021)
- [Theory on Forgetting and Generalization of Continual Learning](https://mlsanity.com/paper/2302.05836/) (2023)

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

- [Understanding Head Geometry and Dynamics in Federated Regression through a Natural Solution Selection Rule: An Unconstrained Feature Model Analysis](https://mlsanity.com/paper/2609.39464/) (2026)

## Abstract (arXiv)

In distributed training of machine learning models, gradient descent with local iterative steps, commonly known as Local (Stochastic) Gradient Descent (Local-(S)GD) or Federated averaging (FedAvg), is a very popular method to mitigate communication burden. In this method, gradient steps based on local datasets are taken independently in distributed compute nodes to update the local models, which are then aggregated intermittently. In the interpolation regime, Local-GD can converge to zero training loss. However, with many potential solutions corresponding to zero training loss, it is not known which solution Local-GD converges to. In this work we answer this question by analyzing implicit bias of Local-GD for classification tasks with linearly separable data. For the interpolation regime, our analysis shows that the aggregated global model obtained from Local-GD, with arbitrary number of local steps, converges exactly to the model that would be obtained if all data were in one place (centralized model) ''in direction''. Our result gives the exact rate of convergence to the centralized model with respect to the number of local steps. We also obtain the same implicit bias with a learning rate independent of number of local steps with a modified version of the Local-GD algorithm. Our analysis provides a new view to understand why Local-GD can still perform well with a very large number of local steps even for heterogeneous data. Lastly, we also discuss the extension of our results to Local-SGD and non-separable data.