# Tighter Regret Analysis and Optimization of Online Federated Learning

arXiv: https://arxiv.org/abs/2205.06491 · HTML: https://mlsanity.com/paper/2205.06491/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 42 references that are in the map.
- First posted on arXiv 13 May 2022.

## Builds on (most cited first, 22 of 22)

- [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 with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Federated Learning for Mobile Keyboard Prediction](https://mlsanity.com/paper/1811.03604/) (2018)
- [Federated Machine Learning: Concept and Applications](https://mlsanity.com/paper/1902.04885/) (2019)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [QSGD: Communication-Efficient SGD via Gradient Quantization and Encoding](https://mlsanity.com/paper/1610.02132/) (2016)
- [UVeQFed: Universal Vector Quantization for Federated Learning](https://mlsanity.com/paper/2006.03262/) (2020)
- [Federated Learning: Opportunities and Challenges](https://mlsanity.com/paper/2101.05428/) (2021)
- [Variance Reduced Local SGD with Lower Communication Complexity](https://mlsanity.com/paper/1912.12844/) (2019)
- [FedIPR: Ownership Verification for Federated Deep Neural Network Models](https://mlsanity.com/paper/2109.13236/) (2021)
- [Random Feature-based Online Multi-kernel Learning in Environments with Unknown Dynamics](https://mlsanity.com/paper/1712.09983/) (2017)
- [UAV-assisted Online Machine Learning over Multi-Tiered Networks: A Hierarchical Nested Personalized Federated Learning Approach](https://mlsanity.com/paper/2106.15734/) (2021)
- [Communication-Efficient Online Federated Learning Framework for Nonlinear Regression](https://mlsanity.com/paper/2110.06556/) (2021)
- [Federated Learning for Localization: A Privacy-Preserving Crowdsourcing Method](https://mlsanity.com/paper/2001.01911/) (2020)
- [Distributed Online Learning with Multiple Kernels](https://mlsanity.com/paper/2102.12733/) (2021)
- [FedVQCS: Federated Learning via Vector Quantized Compressed Sensing](https://mlsanity.com/paper/2204.07692/) (2022)
- [Active Learning with Multiple Kernels](https://mlsanity.com/paper/2005.03188/) (2020)

## Built on by (most cited first, 14 of 14)

- [Online Vertical Federated Learning for Cooperative Spectrum Sensing](https://mlsanity.com/paper/2312.11363/) (2023)
- [On the Necessity of Collaboration for Online Model Selection with Decentralized Data](https://mlsanity.com/paper/2404.09494/) (2024)
- [Review of Mathematical Optimization in Federated Learning](https://mlsanity.com/paper/2412.01630/) (2024)
- [Regret-Optimal Federated Transfer Learning for Kernel Regression with Applications in American Option Pricing](https://mlsanity.com/paper/2309.04557/) (2023)
- [Multimodal Online Federated Learning with Modality Missing in Internet of Things](https://mlsanity.com/paper/2505.16138/) (2025)
- [Mitigating Modality Quantity and Quality Imbalance in Multimodal Online Federated Learning](https://mlsanity.com/paper/2508.11159/) (2025)
- [Federated Online Prediction from Experts with Differential Privacy: Separations and Regret Speed-ups](https://mlsanity.com/paper/2409.19092/) (2024)
- [Hi-SAFE: Hierarchical Secure Aggregation for Lightweight Federated Learning](https://mlsanity.com/paper/2511.18887/) (2025)
- [Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum](https://mlsanity.com/paper/2504.12742/) (2025)
- [Event-Driven Online Vertical Federated Learning](https://mlsanity.com/paper/2506.14911/) (2025)
- [Federated Reinforcement Learning in Heterogeneous Environments](https://mlsanity.com/paper/2507.14487/) (2025)
- [FedSEA: Achieving Benefit of Parallelization in Federated Online Learning](https://mlsanity.com/paper/2604.19336/) (2026)
- [OmniISR: A Unified Framework for Centralized and Federated Learning via Intermediate Supervision and Regularization](https://mlsanity.com/paper/2605.20276/) (2026)
- [Parameter Efficient Multi-Class Intelligent Scheduling for Multimodal Online Distributed Industrial Anomaly Detection](https://mlsanity.com/paper/2605.23984/) (2026)

## Abstract (arXiv)

In federated learning (FL), it is commonly assumed that all data are placed at clients in the beginning of machine learning (ML) optimization (i.e., offline learning). However, in many real-world applications, it is expected to proceed in an online fashion. To this end, online FL (OFL) has been introduced, which aims at learning a sequence of global models from decentralized streaming data such that the so-called cumulative regret is minimized. Combining online gradient descent and model averaging, in this framework, FedOGD is constructed as the counterpart of FedSGD in FL. While it can enjoy an optimal sublinear regret, FedOGD suffers from heavy communication costs. In this paper, we present a communication-efficient method (named OFedIQ) by means of intermittent transmission (enabled by client subsampling and periodic transmission) and quantization. For the first time, we derive the regret bound that captures the impact of data-heterogeneity and the communication-efficient techniques. Through this, we efficiently optimize the parameters of OFedIQ such as sampling rate, transmission period, and quantization levels. Also, it is proved that the optimized OFedIQ can asymptotically achieve the performance of FedOGD while reducing the communication costs by 99%. Via experiments with real datasets, we demonstrate the effectiveness of the optimized OFedIQ.