# Federated Submodel Optimization for Hot and Cold Data Features

arXiv: https://arxiv.org/abs/2109.07704 · HTML: https://mlsanity.com/paper/2109.07704/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 16 Sep 2021.

## Builds on (most cited first, 17 of 17)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [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)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Deep Interest Network for Click-Through Rate Prediction](https://mlsanity.com/paper/1706.06978/) (2017)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [Client Selection in Federated Learning: Convergence Analysis and Power-of-Choice Selection Strategies](https://mlsanity.com/paper/2010.01243/) (2020)
- [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)
- [D2: Decentralized Training over Decentralized Data](https://mlsanity.com/paper/1803.07068/) (2018)
- [Clustered Sampling: Low-Variance and Improved Representativity for Clients Selection in Federated Learning](https://mlsanity.com/paper/2105.05883/) (2021)
- [First Analysis of Local GD on Heterogeneous Data](https://mlsanity.com/paper/1909.04715/) (2019)
- [Equilibrated adaptive learning rates for non-convex optimization](https://mlsanity.com/paper/1502.04390/) (2015)
- [On the Computation and Communication Complexity of Parallel SGD with Dynamic Batch Sizes for Stochastic Non-Convex Optimization](https://mlsanity.com/paper/1905.04346/) (2019)
- [Efficient Twitter Sentiment Classification using Subjective Distant Supervision](https://mlsanity.com/paper/1701.03051/) (2017)

## Built on by (most cited first, 4 of 4)

- [FedDisco: Federated Learning with Discrepancy-Aware Collaboration](https://mlsanity.com/paper/2305.19229/) (2023)
- [Collaborative Learning of On-Device Small Model and Cloud-Based Large Model: Advances and Future Directions](https://mlsanity.com/paper/2504.15300/) (2025)
- [FedKLPR: KL-Guided Pruning-Aware Federated Learning for Person Re-Identification](https://mlsanity.com/paper/2508.17431/) (2025)
- [A Taxonomy and Resolution Strategy for Client-Level Disagreements in Federated Learning](https://mlsanity.com/paper/2604.23386/) (2026)

## Abstract (arXiv)

We study practical data characteristics underlying federated learning, where non-i.i.d. data from clients have sparse features, and a certain client's local data normally involves only a small part of the full model, called a submodel. Due to data sparsity, the classical federated averaging (FedAvg) algorithm or its variants will be severely slowed down, because when updating the global model, each client's zero update of the full model excluding its submodel is inaccurately aggregated. Therefore, we propose federated submodel averaging (FedSubAvg), ensuring that the expectation of the global update of each model parameter is equal to the average of the local updates of the clients who involve it. We theoretically proved the convergence rate of FedSubAvg by deriving an upper bound under a new metric called the element-wise gradient norm. In particular, this new metric can characterize the convergence of federated optimization over sparse data, while the conventional metric of squared gradient norm used in FedAvg and its variants cannot. We extensively evaluated FedSubAvg over both public and industrial datasets. The evaluation results demonstrate that FedSubAvg significantly outperforms FedAvg and its variants.