# FedVeca: Federated Vectorized Averaging on Non-IID Data with Adaptive Bi-directional Global Objective

arXiv: https://arxiv.org/abs/2209.13803 · HTML: https://mlsanity.com/paper/2209.13803/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 28 Sep 2022.

## Builds on (most cited first, 29 of 29)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [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)
- [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)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Ensemble Distillation for Robust Model Fusion in Federated Learning](https://mlsanity.com/paper/2006.07242/) (2020)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Robust and Communication-Efficient Federated Learning from Non-IID Data](https://mlsanity.com/paper/1903.02891/) (2019)
- [Adaptive Federated Learning in Resource Constrained Edge Computing Systems](https://mlsanity.com/paper/1804.05271/) (2018)
- [Data-Free Knowledge Distillation for Heterogeneous Federated Learning](https://mlsanity.com/paper/2105.10056/) (2021)
- [Federated Learning on Non-IID Data: A Survey](https://mlsanity.com/paper/2106.06843/) (2021)
- [No Fear of Heterogeneity: Classifier Calibration for Federated Learning with Non-IID Data](https://mlsanity.com/paper/2106.05001/) (2021)
- [FedDC: Federated Learning with Non-IID Data via Local Drift Decoupling and Correction](https://mlsanity.com/paper/2203.11751/) (2022)
- [Federated Meta-Learning with Fast Convergence and Efficient Communication](https://mlsanity.com/paper/1802.07876/) (2018)
- [Federated Adversarial Domain Adaptation](https://mlsanity.com/paper/1911.02054/) (2019)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [FedMix: Approximation of Mixup under Mean Augmented Federated Learning](https://mlsanity.com/paper/2107.00233/) (2021)
- [Tight Analyses for Non-Smooth Stochastic Gradient Descent](https://mlsanity.com/paper/1812.05217/) (2018)
- [Variance Reduced Local SGD with Lower Communication Complexity](https://mlsanity.com/paper/1912.12844/) (2019)
- [Variational Federated Multi-Task Learning](https://mlsanity.com/paper/1906.06268/) (2019)
- [From Distributed Machine Learning to Federated Learning: A Survey](https://mlsanity.com/paper/2104.14362/) (2021)
- [Federated learning with class imbalance reduction](https://mlsanity.com/paper/2011.11266/) (2020)
- [Stochastic Gradient Descent for Nonconvex Learning without Bounded Gradient Assumptions](https://mlsanity.com/paper/1902.00908/) (2019)
- [Mitigating Data Heterogeneity in Federated Learning with Data Augmentation](https://mlsanity.com/paper/2206.09979/) (2022)

## Abstract (arXiv)

Federated Learning (FL) is a distributed machine learning framework to alleviate the data silos, where decentralized clients collaboratively learn a global model without sharing their private data. However, the clients' Non-Independent and Identically Distributed (Non-IID) data negatively affect the trained model, and clients with different numbers of local updates may cause significant gaps to the local gradients in each communication round. In this paper, we propose a Federated Vectorized Averaging (FedVeca) method to address the above problem on Non-IID data. Specifically, we set a novel objective for the global model which is related to the local gradients. The local gradient is defined as a bi-directional vector with step size and direction, where the step size is the number of local updates and the direction is divided into positive and negative according to our definition. In FedVeca, the direction is influenced by the step size, thus we average the bi-directional vectors to reduce the effect of different step sizes. Then, we theoretically analyze the relationship between the step sizes and the global objective, and obtain upper bounds on the step sizes per communication round. Based on the upper bounds, we design an algorithm for the server and the client to adaptively adjusts the step sizes that make the objective close to the optimum. Finally, we conduct experiments on different datasets, models and scenarios by building a prototype system, and the experimental results demonstrate the effectiveness and efficiency of the FedVeca method.