# Is Local SGD Better than Minibatch SGD?

arXiv: https://arxiv.org/abs/2002.07839 · HTML: https://mlsanity.com/paper/2002.07839/

## Key facts

- Cited by 151 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2020.

## Built on by (most cited first, 30 of 151)

- [Federated Learning with Buffered Asynchronous Aggregation](https://mlsanity.com/paper/2106.06639/) (2021)
- [ProxSkip: Yes! Local Gradient Steps Provably Lead to Communication Acceleration! Finally!](https://mlsanity.com/paper/2202.09357/) (2022)
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- [Preservation of the Global Knowledge by Not-True Distillation in Federated Learning](https://mlsanity.com/paper/2106.03097/) (2021)
- [FedVARP: Tackling the Variance Due to Partial Client Participation in Federated Learning](https://mlsanity.com/paper/2207.14130/) (2022)
- [Asynchronous SGD Beats Minibatch SGD Under Arbitrary Delays](https://mlsanity.com/paper/2206.07638/) (2022)
- [FedAvg with Fine Tuning: Local Updates Lead to Representation Learning](https://mlsanity.com/paper/2205.13692/) (2022)
- [Convergence and Accuracy Trade-Offs in Federated Learning and Meta-Learning](https://mlsanity.com/paper/2103.05032/) (2021)
- [Dynamic Regularized Sharpness Aware Minimization in Federated Learning: Approaching Global Consistency and Smooth Landscape](https://mlsanity.com/paper/2305.11584/) (2023)
- [A Unified Analysis of Federated Learning with Arbitrary Client Participation](https://mlsanity.com/paper/2205.13648/) (2022)
- [STEM: A Stochastic Two-Sided Momentum Algorithm Achieving Near-Optimal Sample and Communication Complexities for Federated Learning](https://mlsanity.com/paper/2106.10435/) (2021)
- [Differentially Private Low-Rank Adaptation of Large Language Model Using Federated Learning](https://mlsanity.com/paper/2312.17493/) (2023)
- [Local Stochastic Gradient Descent Ascent: Convergence Analysis and Communication Efficiency](https://mlsanity.com/paper/2102.13152/) (2021)
- [Sharp Bounds for Federated Averaging (Local SGD) and Continuous Perspective](https://mlsanity.com/paper/2111.03741/) (2021)
- [On the Unreasonable Effectiveness of Federated Averaging with Heterogeneous Data](https://mlsanity.com/paper/2206.04723/) (2022)
- [Moshpit SGD: Communication-Efficient Decentralized Training on Heterogeneous Unreliable Devices](https://mlsanity.com/paper/2103.03239/) (2021)
- [Faster Adaptive Federated Learning](https://mlsanity.com/paper/2212.00974/) (2022)
- [Asynchronous Stochastic Optimization Robust to Arbitrary Delays](https://mlsanity.com/paper/2106.11879/) (2021)
- [The Min-Max Complexity of Distributed Stochastic Convex Optimization with Intermittent Communication](https://mlsanity.com/paper/2102.01583/) (2021)
- [Bias-Variance Reduced Local SGD for Less Heterogeneous Federated Learning](https://mlsanity.com/paper/2102.03198/) (2021)
- [On the Convergence of Federated Averaging with Cyclic Client Participation](https://mlsanity.com/paper/2302.03109/) (2023)
- [Private Federated Learning Without a Trusted Server: Optimal Algorithms for Convex Losses](https://mlsanity.com/paper/2106.09779/) (2021)
- [FedDR -- Randomized Douglas-Rachford Splitting Algorithms for Nonconvex Federated Composite Optimization](https://mlsanity.com/paper/2103.03452/) (2021)
- [Implicit Gradient Alignment in Distributed and Federated Learning](https://mlsanity.com/paper/2106.13897/) (2021)
- [3PC: Three Point Compressors for Communication-Efficient Distributed Training and a Better Theory for Lazy Aggregation](https://mlsanity.com/paper/2202.00998/) (2022)
- [Private Non-Convex Federated Learning Without a Trusted Server](https://mlsanity.com/paper/2203.06735/) (2022)
- [Personalized Federated Learning for Heterogeneous Clients with Clustered Knowledge Transfer](https://mlsanity.com/paper/2109.08119/) (2021)
- [Towards Federated Learning on Time-Evolving Heterogeneous Data](https://mlsanity.com/paper/2112.13246/) (2021)

## Abstract (arXiv)

We study local SGD (also known as parallel SGD and federated averaging), a natural and frequently used stochastic distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch SGD. (1) For quadratic objectives we prove that local SGD strictly dominates minibatch SGD and that accelerated local SGD is minimax optimal for quadratics; (2) For general convex objectives we provide the first guarantee that at least sometimes improves over minibatch SGD; (3) We show that indeed local SGD does not dominate minibatch SGD by presenting a lower bound on the performance of local SGD that is worse than the minibatch SGD guarantee.