# Convergence of Distributed Adaptive Optimization with Local Updates

arXiv: https://arxiv.org/abs/2409.13155 · HTML: https://mlsanity.com/paper/2409.13155/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Sep 2024.

## Built on by (most cited first, 10 of 10)

- [MuLoCo: Muon is a practical inner optimizer for DiLoCo](https://mlsanity.com/paper/2505.23725/) (2025)
- [Overcoming the Communication-Performance Tradeoff in LLM Pretraining](https://mlsanity.com/paper/2508.15706/) (2025)
- [DES-LOC: Desynced Low Communication Adaptive Optimizers for Training Foundation Models](https://mlsanity.com/paper/2505.22549/) (2025)
- [MT-DAO: Multi-Timescale Distributed Adaptive Optimizers with Local Updates](https://mlsanity.com/paper/2510.05361/) (2025)
- [Rethinking LoRA for Data Heterogeneous Federated Learning: Subspace and State Alignment](https://mlsanity.com/paper/2602.01746/) (2026)
- [LoRDO: Distributed Low-Rank Optimization with Infrequent Communication](https://mlsanity.com/paper/2602.04396/) (2026)
- [Photon: Federated LLM Pre-Training](https://mlsanity.com/paper/2411.02908/) (2024)
- [Understanding Generalization of Federated Learning: the Trade-off between Model Stability and Optimization](https://mlsanity.com/paper/2411.16303/) (2024)
- [DualOptim+: Bridging Shared and Decoupled Optimizer States for Better Machine Unlearning in Large Language Models](https://mlsanity.com/paper/2605.21539/) (2026)
- [FoMoE: Breaking the Full-Replica Barrier with a Federation of MoEs](https://mlsanity.com/paper/2606.19025/) (2026)

## Abstract (arXiv)

We study distributed adaptive algorithms with local updates (intermittent communication). Despite the great empirical success of adaptive methods in distributed training of modern machine learning models, the theoretical benefits of local updates within adaptive methods, particularly in terms of reducing communication complexity, have not been fully understood yet. In this paper, for the first time, we prove that em Local SGD em with momentum (em Local em SGDM) and em Local em Adam can outperform their minibatch counterparts in convex and weakly convex settings in certain regimes, respectively. Our analysis relies on a novel technique to prove contraction during local iterations, which is a crucial yet challenging step to show the advantages of local updates, under generalized smoothness assumption and gradient clipping strategy.