FedBCD:Communication-Efficient Accelerated Block Coordinate Gradient Descent for Federated Learning

Federated learning (FL) is an emerging distributed machine learning paradigm that enables local devices to jointly train a global model while keeping data decentralized and private. We propose a variance-reduction based algorithm, VRA-FedSGD, for FL in the presence of heavy-tailed gradient noise and communication noise, where these noises are prevalent in large-scale machine learning over wireless networks and Internet of Things deployments. VRA-FedSGD employs a momentum variance reduction technique together with a nonlinear mapping to mitigate heavy-tailed gradient noise, and uses a variance-reduced aggregation mechanism to suppress heavy-tailed communication noise. In the mean sense, VRA-FedSGD achieves a convergence rate of {\small$\mathcal{O}\left(K^{-(p-1)/(2p-1)}\right)$} for nonconvex objective functions, where $p$ is the tail index of heavy-tailed noise. In the almost sure sense, VRA-FedSGD achieves a convergence rate of $\tilde{\mathcal{O}}\left(K^{-(1-1/(p-ε))}\right)$ for strongly convex objective functions, where $ε$ is an arbitrarily small constant. Simulated experiments on a logistic regression problem with real-world data verify the effectiveness of VRA-FedSGD.

Federated learning (FL) enables collaborative model training without sharing raw patient data, but standard approaches such as FedAvg treat each client as a black box and provide no mechanism for isolating an adversarial contributor, auditing per-client influence, or honoring a departed participant's right to be forgotten. We present Fed-FBD (Federated Functional Block Diversification), a modular federated architecture that decomposes a ResNet backbone into six functional blocks (the stem, four residual groups, and the classification head) and maintains a warehouse of N color variants, each assembled from independently tracked and contributor-stamped blocks. Fed-FBD provides three capabilities absent in FedAvg: (i) architecturally guaranteed block-level isolation, so that an adversarial or mislabelled client cannot contaminate the clean colous; (ii) privacy-by-design, where membership inference advantage is already indistinguishable from chance before any privacy mechanism is applied; and (iii) surgical machine unlearning of a departed participant's contribution at sub-second cost and without retraining. Experiments on six MedMNIST-2D datasets, PathMNIST at 224x224, and CIFAR-10 show that Fed-FBD trades a modest 0.3%-3.1% IID accuracy gap on the adequately sized datasets for these guarantees, remains within 0.8%-4.0% of FedAvg at Dirichlet alpha=1.0 on three of four datasets, and confines all six adversarial attacks we study to the poisoned client's own blocks with at most +/-0.01 AUC drift on the clean colors.

Federated training of foundation models is constrained by client memory and communication costs. LoRA-based methods reduce these costs through low-rank adapters, but their fixed rank budget can limit adaptation. Gradient low-rank optimization offers greater flexibility, yet independently chosen client subspaces create a problem we term subspace fragmentation: local projections interact with data heterogeneity to bias aggregated directions, while aggregation can increase update rank and communication cost. Thus, accurate local gradient compression need not preserve global descent. We propose FedLore, which shares a low-rank optimization basis within each round and refreshes it across rounds. The shared basis enables exact aggregation in low-rank coordinates and eliminates the identified projection bias. Subspace refresh allows the accumulated model update to exceed the per-round rank budget. We characterize the aggregation bias and establish an $O(T^{-1/2})$ stationarity bound for the projected-SGD variant under a global-gradient coverage condition and standard smoothness and variance assumptions, with bounded gradient heterogeneity. Experiments on vision and language tasks, including federated pre-training, show that FedLore outperforms the evaluated low-rank adapter baselines and matches or exceeds full-parameter training, while reducing communication and optimizer-state memory.