Dimensionality Reduction for Robust Federated Learning: A Theoretical Analysis and Convergence Guarantee
arXiv:2605.28335v2 Announce Type: replace Abstract: Federated Learning (FL) enables multiple clients to collaboratively train models without sharing raw data, but it is highly vulnerable to Byzantine attacks. Existing robust approaches can neutralize these threats but incur substantial computational overhead during high-dimensional gradient aggregation, an overhead that scales poorly with model size and increasingly dominates the training cost as modern models grow larger. To address this computational bottleneck, we propose Projected Dimensionality Reduction (PDR), a universal acceleration framework for vector-level distance-based robust aggregators, which performs robust aggregation by compressing gradients into a drastically smaller subspace via sparse random projection to efficiently compute reliability weights. This approach reduces the server computational complexity to an optimal $ \mathcal{O}(Mp) $, where $ M $ is the number of clients and $ p $ is the model dimension, matching