# Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization

arXiv: https://arxiv.org/abs/2007.07481 · HTML: https://mlsanity.com/paper/2007.07481/

## Key facts

- Cited by 906 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2020.

## Built on by (most cited first, 30 of 906)

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- [FedProto: Federated Prototype Learning across Heterogeneous Clients](https://mlsanity.com/paper/2105.00243/) (2021)
- [Federated Learning on Non-IID Data: A Survey](https://mlsanity.com/paper/2106.06843/) (2021)
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- [No Fear of Heterogeneity: Classifier Calibration for Federated Learning with Non-IID Data](https://mlsanity.com/paper/2106.05001/) (2021)
- [FjORD: Fair and Accurate Federated Learning under heterogeneous targets with Ordered Dropout](https://mlsanity.com/paper/2102.13451/) (2021)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
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- [OpenFedLLM: Training Large Language Models on Decentralized Private Data via Federated Learning](https://mlsanity.com/paper/2402.06954/) (2024)
- [Linear Convergence in Federated Learning: Tackling Client Heterogeneity and Sparse Gradients](https://mlsanity.com/paper/2102.07053/) (2021)
- [FedALA: Adaptive Local Aggregation for Personalized Federated Learning](https://mlsanity.com/paper/2212.01197/) (2022)
- [FairFed: Enabling Group Fairness in Federated Learning](https://mlsanity.com/paper/2110.00857/) (2021)
- [Local Learning Matters: Rethinking Data Heterogeneity in Federated Learning](https://mlsanity.com/paper/2111.14213/) (2021)
- [Federated Learning with Label Distribution Skew via Logits Calibration](https://mlsanity.com/paper/2209.00189/) (2022)
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- [Clustered Sampling: Low-Variance and Improved Representativity for Clients Selection in Federated Learning](https://mlsanity.com/paper/2105.05883/) (2021)
- [Federated Learning on Non-IID Graphs via Structural Knowledge Sharing](https://mlsanity.com/paper/2211.13009/) (2022)
- [Preservation of the Global Knowledge by Not-True Distillation in Federated Learning](https://mlsanity.com/paper/2106.03097/) (2021)
- [FedProc: Prototypical Contrastive Federated Learning on Non-IID data](https://mlsanity.com/paper/2109.12273/) (2021)
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- [FedCM: Federated Learning with Client-level Momentum](https://mlsanity.com/paper/2106.10874/) (2021)
- [FedBiOT: LLM Local Fine-tuning in Federated Learning without Full Model](https://mlsanity.com/paper/2406.17706/) (2024)

## Abstract (arXiv)

In federated optimization, heterogeneity in the clients' local datasets and computation speeds results in large variations in the number of local updates performed by each client in each communication round. Naive weighted aggregation of such models causes objective inconsistency, that is, the global model converges to a stationary point of a mismatched objective function which can be arbitrarily different from the true objective. This paper provides a general framework to analyze the convergence of federated heterogeneous optimization algorithms. It subsumes previously proposed methods such as FedAvg and FedProx and provides the first principled understanding of the solution bias and the convergence slowdown due to objective inconsistency. Using insights from this analysis, we propose FedNova, a normalized averaging method that eliminates objective inconsistency while preserving fast error convergence.