# A General Theory for Federated Optimization with Asynchronous and Heterogeneous Clients Updates

arXiv: https://arxiv.org/abs/2206.10189 · HTML: https://mlsanity.com/paper/2206.10189/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 49 references that are in the map.
- First posted on arXiv 21 Jun 2022.

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [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)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [Client Selection for Federated Learning with Heterogeneous Resources in Mobile Edge](https://mlsanity.com/paper/1804.08333/) (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)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication](https://mlsanity.com/paper/1902.00340/) (2019)
- [Client Selection in Federated Learning: Convergence Analysis and Power-of-Choice Selection Strategies](https://mlsanity.com/paper/2010.01243/) (2020)
- [Federated Learning with Buffered Asynchronous Aggregation](https://mlsanity.com/paper/2106.06639/) (2021)
- [AdaGrad stepsizes: Sharp convergence over nonconvex landscapes](https://mlsanity.com/paper/1806.01811/) (2018)
- [Qsparse-local-SGD: Distributed SGD with Quantization, Sparsification, and Local Computations](https://mlsanity.com/paper/1906.02367/) (2019)
- [On the Linear Speedup Analysis of Communication Efficient Momentum SGD for Distributed Non-Convex Optimization](https://mlsanity.com/paper/1905.03817/) (2019)
- [Asynchronous Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1710.06952/) (2017)
- [On the Convergence of Stochastic Gradient Descent with Adaptive Stepsizes](https://mlsanity.com/paper/1805.08114/) (2018)
- [ATOMO: Communication-efficient Learning via Atomic Sparsification](https://mlsanity.com/paper/1806.04090/) (2018)
- [SlowMo: Improving Communication-Efficient Distributed SGD with Slow Momentum](https://mlsanity.com/paper/1910.00643/) (2019)
- [Asynchronous Parallel Stochastic Gradient for Nonconvex Optimization](https://mlsanity.com/paper/1506.08272/) (2015)
- [Decentralized Deep Learning with Arbitrary Communication Compression](https://mlsanity.com/paper/1907.09356/) (2019)
- [SGD and Hogwild! Convergence Without the Bounded Gradients Assumption](https://mlsanity.com/paper/1802.03801/) (2018)
- [Asynchronous Federated Learning on Heterogeneous Devices: A Survey](https://mlsanity.com/paper/2109.04269/) (2021)

## Built on by (most cited first, 17 of 17)

- [FedFa: A Fully Asynchronous Training Paradigm for Federated Learning](https://mlsanity.com/paper/2404.11015/) (2024)
- [Achieving Linear Speedup in Asynchronous Federated Learning with Heterogeneous Clients](https://mlsanity.com/paper/2402.11198/) (2024)
- [Queuing dynamics of asynchronous Federated Learning](https://mlsanity.com/paper/2405.00017/) (2024)
- [FedStale: leveraging stale client updates in federated learning](https://mlsanity.com/paper/2405.04171/) (2024)
- [FedStaleWeight: Buffered Asynchronous Federated Learning with Fair Aggregation via Staleness Reweighting](https://mlsanity.com/paper/2406.02877/) (2024)
- [Ringleader ASGD: The First Asynchronous SGD with Optimal Time Complexity under Data Heterogeneity](https://mlsanity.com/paper/2509.22860/) (2025)
- [Scheduling for On-Board Federated Learning with Satellite Clusters](https://mlsanity.com/paper/2402.09105/) (2024)
- [Asynchronous Federated Stochastic Optimization for Heterogeneous Objectives Under Arbitrary Delays](https://mlsanity.com/paper/2405.10123/) (2024)
- [FAVANO: Federated AVeraging with Asynchronous NOdes](https://mlsanity.com/paper/2305.16099/) (2023)
- [Dual-Delayed Asynchronous SGD for Arbitrarily Heterogeneous Data](https://mlsanity.com/paper/2405.16966/) (2024)
- [Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Framework](https://mlsanity.com/paper/2502.00846/) (2025)
- [Online Federation For Mixtures of Proprietary Agents with Black-Box Encoders](https://mlsanity.com/paper/2505.00216/) (2025)
- [Adaptive Deadline and Batch Layered Synchronized Federated Learning](https://mlsanity.com/paper/2505.23973/) (2025)
- [Federated Learning based on Pruning and Recovery](https://mlsanity.com/paper/2403.15439/) (2024)
- [Analysis of Asynchronous Federated Learning: Unraveling the Interactions between Gradient Compression, Delay, and Data Heterogeneity](https://mlsanity.com/paper/2504.19903/) (2025)
- [Scalable Asynchronous Federated Modeling for Spatial Data](https://mlsanity.com/paper/2510.01771/) (2025)
- [FedQueue: Queue-Aware Federated Learning for Cross-Facility HPC Training](https://mlsanity.com/paper/2605.02125/) (2026)

## Abstract (arXiv)

We propose a novel framework to study asynchronous federated learning optimization with delays in gradient updates. Our theoretical framework extends the standard FedAvg aggregation scheme by introducing stochastic aggregation weights to represent the variability of the clients update time, due for example to heterogeneous hardware capabilities. Our formalism applies to the general federated setting where clients have heterogeneous datasets and perform at least one step of stochastic gradient descent (SGD). We demonstrate convergence for such a scheme and provide sufficient conditions for the related minimum to be the optimum of the federated problem. We show that our general framework applies to existing optimization schemes including centralized learning, FedAvg, asynchronous FedAvg, and FedBuff. The theory here provided allows drawing meaningful guidelines for designing a federated learning experiment in heterogeneous conditions. In particular, we develop in this work FedFix, a novel extension of FedAvg enabling efficient asynchronous federated training while preserving the convergence stability of synchronous aggregation. We empirically demonstrate our theory on a series of experiments showing that asynchronous FedAvg leads to fast convergence at the expense of stability, and we finally demonstrate the improvements of FedFix over synchronous and asynchronous FedAvg.