Skip to main content
Log in

Robust federated learning aggregation for highly heterogeneous data

  • Published:
Cluster Computing Aims and scope Submit manuscript

Abstract

Federated learning (FL) is a distributed learning approach in which clients collaboratively train a machine learning model without sharing data. While this distributed learning paradigm has clear benefits in terms of privacy, data heterogeneity among clients strengthens the local client drift causing the degradation of global model’s performance. Since gradient distances can be used to quantify the local client drift, we leverage them in the aggregation strategy to achieve robust performance in highly heterogeneous environments. In this work, we propose two adaptive aggregation algorithms that optimize the aggregation weights based on cross-rounds and cross-clients gradient distances, dubbed CROG and CLIG, respectively. Through extensive experiments using various datasets, we verify that the proposed algorithms outperform conventional FL methods, confirming that the proposed aggregation weights are formed close to the optimal aggregation weights and operate robustly in extreme non-IID data environments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+
from €37.37 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price includes VAT (Netherlands)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Algorithm 1
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability

No datasets were generated or analysed during the current study.

References

  1. McMahan, B., Moore, E., Ramage, D., Hampson, S., Arcas, B.A.: Communication-efficient learning of deep networks from decentralized data. In: Singh, A., Zhu, J. (eds.) Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, pp. 1273–1282 (2017). PMLR

  2. Wang, J., Liu, Q., Liang, H., Joshi, G., Poor, H.V.: Tackling the objective inconsistency problem in heterogeneous federated optimization. Adv. Neural. Inf. Process. Syst. 33, 7611–7623 (2020)

    Google Scholar 

  3. Hsu, T.-M.H., Qi, H., Brown, M.: Measuring the effects of non-identical data distribution for federated visual classification, (2019). arXiv preprint arXiv:1909.06335

  4. Zhao, Y., Li, M., Lai, L., Suda, N., Civin, D., Chandra, V.: Federated learning with non-iid data, (2018). arXiv preprint arXiv:1806.00582

  5. Li, T., Sahu, A.K., Zaheer, M., Sanjabi, M., Talwalkar, A., Smith, V.: Federated optimization in heterogeneous networks. Proc. Mach. learning syst. 2, 429–450 (2020)

    Google Scholar 

  6. Karimireddy, S.P., Kale, S., Mohri, M., Reddi, S., Stich, S., Suresh, A.T.: Scaffold: Stochastic controlled averaging for federated learning. In: International Conference on Machine Learning, pp. 5132–5143. (2020). (PMLR)

  7. Reyes, J., Di Jorio, L., Low-Kam, C., Kersten-Oertel, M.: Precision-weighted federated learning, (2021). arXiv preprint arXiv:2107.09627

  8. Zeng, Y., Mu, Y., Yuan, J., Teng, S., Zhang, J., Wan, J., Ren, Y., Zhang, Y.: Adaptive federated learning with non-iid data. Comput. J. 66(11), 2758–2772 (2023)

    Article  Google Scholar 

  9. Li, Z., Lin, T., Shang, X., Wu, C.: Revisiting weighted aggregation in federated learning with neural networks. In: Krause, A., Brunskill, E., Cho, K., Engelhardt, B., Sabato, S., Scarlett, J. (eds.) Proceedings of the 40th International Conference on Machine Learning, pp. 19767–19788. JMLR.org, Honolulu, Hawaii, USA (2023)

  10. Rehman, Y.A.U., Gao, Y., Gusmao, P.P.B., Alibeigi, M., Shen, J., Lane, N.D.: L-dawa: Layer-wise divergence aware weight aggregation in federated self-supervised visual representation learning. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 16464–16473. (2023)

  11. Wu, H., Wang, P.: Fast-convergent federated learning with adaptive weighting. IEEE Trans. Cognitive Commun. Netw. 7(4), 1078–1088 (2021)

    Article  Google Scholar 

  12. Acar, D.A.E., Zhao, Y., Navarro, R.M., Mattina, M., Whatmough, P.N., Saligrama, V.: Federated learning based on dynamic regularization, (2021). arXiv preprint arXiv:2111.04263

  13. Li, Q., He, B., Song, D.: Model-contrastive federated learning. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 10713–10722. (2021)

  14. Xiao, C., et al.: Confusion-resistant federated learning via diffusion-based data harmonization on non-iid data. Adv. Neural. Inf. Process. Syst. 37, 137495–137520 (2024)

    Google Scholar 

  15. Reddi, S., Charles, Z., Zaheer, M., Garrett, Z., Rush, K., Konečnỳ, J., Kumar, S., McMahan, H.B.: Adaptive federated optimization. arXiv preprint arXiv:2003.00295 (2020)

  16. Lin, T., Kong, L., Stich, S.U., Jaggi, M.: Ensemble distillation for robust model fusion in federated learning. Adv. Neural. Inf. Process. Syst. 33, 2351–2363 (2020)

    Google Scholar 

  17. Liu, X., Liu, L., Ye, F., Shen, Y., Li, X., Jiang, L., Li, J.: Fedlpa: One-shot federated learning with layer-wise posterior aggregation. Adv. Neural. Inf. Process. Syst. 37, 81510–81548 (2024)

    Article  Google Scholar 

  18. Sahoo, P., Tripathi, A., Saha, S., Mondal, S.: FedDUAL: A dual-strategy with adaptive loss and dynamic aggregation for mitigating data heterogeneity in federated learning. Trans. Mach. Learn. Res. (2025)

  19. Mollanejad, A., Ghaffari, A., Seyyedabbasi, A., Navin, A.H.: Fairness-based federated learning in autonomous vehicles with exponential moving average loss weighting. Cluster Comput. 28(10), 627 (2025)

    Article  Google Scholar 

  20. Jain, S., Gupta, S., Pundir, A., Singh, S., Saxena, G.J.: FedA2W: adaptive aggregation with weighted loss proximity for non-iid federated learning. Neural Comput. Appl. 38(13), 561 (2026)

    Article  Google Scholar 

  21. Xiao, H., Rasul, K., Vollgraf, R.: Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms, (2017). arXiv preprint arXiv:1708.07747

  22. Krizhevsky, A., Hinton, G.: Learning multiple layers of features from tiny images, Technical report, University of Toronto, Toronto, ON, Canada (2009)

  23. Tian, P., Liao, W., Yu, W., Blasch, E.: Wscc: A weight-similarity-based client clustering approach for non-iid federated learning. IEEE Internet Things J. 9(20), 20243–20256 (2022)

    Article  Google Scholar 

  24. Jeong, W., Yoon, J., Yang, E., Hwang, S.J.: Federated semi-supervised learning with inter-client consistency & disjoint learning. Int. Conference Learn. Representations (2020)

  25. Li, Y., Wang, S., Chang, T.-H.: Differentially private federated stochastic primal-dual learning for internet of vehicles. IEEE Internet of Things J. 12(11), 17034–17050 (2025)

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by Seoul National University of Science and Technology.

Author information

Authors and Affiliations

Authors

Contributions

Conceptualization: J.B., B.P. and MH.K., Methodology: J.B., B.P. and P.G, Writing: J.B. and B.P., Data Analysis and investigation: J.B and B.P., Software: J.B., B.P. and P.G, Review and editing: MH.K and MC.K., Supervison: MH. K. and MC.K.

Corresponding authors

Correspondence to Minchul Kim or Minhoe Kim.

Ethics declarations

Conflict of interest

The authors have no competing interests to declare that are relevant to the content of this article.

Consent for publication

All authors have read and approved the final manuscript for submission and publication.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bae, J.H., Park, B., Gusmão, P.P.B.d. et al. Robust federated learning aggregation for highly heterogeneous data. Cluster Comput 29, 875 (2026). https://doi.org/10.1007/s10586-026-06716-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Version of record:

  • DOI: https://doi.org/10.1007/s10586-026-06716-3

Keywords