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Such a problem becomes most serious when the distribution of the data among the participants is highly uneven. Based on loss history and exponential weighting, a new algorithm was proposed called EWHFed (Exponential Moving Average in Federated Learning). It takes as input the loss history of the last n rounds, multiplies it by the normalized error of each participant and the gradient he sends to the learner. In such a manner, the algorithm avoids sudden weight updates; this improves both the convergence bound and the actual convergence rate. Furthermore, explicit and implicit exponential weighting for fairness in the learning process allows participants with imbalanced datasets to perform even better. For performance evaluation, the algorithm was tested on the KITTI and GTSRB datasets. From the performance results obtained, the proposed algorithm attained accuracy about 3% higher than the classic FedAvg. Besides, the variance in accuracy by the proposed algorithm is 400 units lower on the KITTI dataset and 300 units lower on the GTSRB dataset compared to other algorithms. It has not only indicated superior stability but also improved fairness towards participants whose data is distributed unevenly.<\/jats:p>","DOI":"10.1007\/s10586-025-05291-3","type":"journal-article","created":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T13:46:44Z","timestamp":1756907204000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fairness-based federated learning in autonomous vehicles with exponential moving average loss weighting"],"prefix":"10.1007","volume":"28","author":[{"given":"Amir","family":"Mollanejad","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali","family":"Ghaffari","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amir","family":"Seyyedabbasi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ahmad Habibizad","family":"Navin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,9,3]]},"reference":[{"issue":"4","key":"5291_CR1","doi-asserted-by":"publisher","first-page":"3363","DOI":"10.1109\/LRA.2019.2926677","volume":"4","author":"J Kabzan","year":"2019","unstructured":"Kabzan, J., et al.: Learning-based model predictive control for autonomous racing. 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