Shiyuan Zuo

Xuming An, Rongfei Fan, Shiyuan Zuo et al.

Federated learning (FL) has emerged as an appealing machine learning approach to deal with massive raw data generated at multiple mobile devices, {which needs to aggregate the training model parameter of every mobile device at one base station (BS) iteratively}. For parameter aggregating in FL, over-the-air computation is a spectrum-efficient solution, which allows all mobile devices to transmit their parameter-mapped signals concurrently to a BS. Due to heterogeneous channel fading and noise, there exists difference between the BS's received signal and its desired signal, measured as the mean-squared error (MSE). To minimize the MSE, we propose to jointly optimize the signal amplification factors at the BS and the mobile devices as well as the data size (the number of data samples involved in local training) at every mobile device. The formulated problem is challenging to solve due to its non-convexity. To find the optimal solution, with some simplification on cost function and variable replacement, which still preserves equivalence, we transform the changed problem to be a bi-level problem equivalently. For the lower-level problem, optimal solution is found by enumerating every candidate solution from the Karush-Kuhn-Tucker (KKT) condition. For the upper-level problem, the optimal solution is found by exploring its piecewise convexity. Numerical results show that our proposed method can greatly reduce the MSE and can help to improve the training performance of FL compared with benchmark methods.

Shiyuan Zuo, Rongfei Fan, Han Hu et al.

In this paper, we propose a robust aggregation method for federated learning (FL) that can effectively tackle malicious Byzantine attacks. At each user, model parameter is firstly updated by multiple steps, which is adjustable over iterations, and then pushed to the aggregation center directly. This decreases the number of interactions between the aggregation center and users, allows each user to set training parameter in a flexible way, and reduces computation burden compared with existing works that need to combine multiple historical model parameters. At the aggregation center, geometric median is leveraged to combine the received model parameters from each user. Rigorous proof shows that zero optimality gap is achieved by our proposed method with linear convergence, as long as the fraction of Byzantine attackers is below half. Numerical results verify the effectiveness of our proposed method.

Rongfei Fan, Xuming An, Shiyuan Zuo et al.

Over-the-air computation is a communication-efficient solution for federated learning (FL). In such a system, iterative procedure is performed: Local gradient of private loss function is updated, amplified and then transmitted by every mobile device; the server receives the aggregated gradient all-at-once, generates and then broadcasts updated model parameters to every mobile device. In terms of amplification factor selection, most related works suppose the local gradient's maximal norm always happens although it actually fluctuates over iterations, which may degrade convergence performance. To circumvent this problem, we propose to turn local gradient to be normalized one before amplifying it. Under our proposed method, when the loss function is smooth, we prove our proposed method can converge to stationary point at sub-linear rate. In case of smooth and strongly convex loss function, we prove our proposed method can achieve minimal training loss at linear rate with any small positive tolerance. Moreover, a tradeoff between convergence rate and the tolerance is discovered. To speedup convergence, problems optimizing system parameters are also formulated for above two cases. Although being non-convex, optimal solution with polynomial complexity of the formulated problems are derived. Experimental results show our proposed method can outperform benchmark methods on convergence performance.

Shiyuan Zuo, Xingrun Yan, Rongfei Fan et al.

Federated Learning (FL) enables multiple clients to collaboratively train models without sharing raw data, but is vulnerable to Byzantine attacks and data heterogeneity, which can severely degrade performance. Existing Byzantine-robust approaches tackle data heterogeneity, but incur high computational overhead during gradient aggregation, thereby slowing down the training process. To address this issue, we propose a simple yet effective Federated Normalized Gradients Algorithm (Fed-NGA), which performs aggregation by merely computing the weighted mean of the normalized gradients from each client. This approach yields a favorable time complexity of $\mathcal{O}(pM)$, where $p$ is the model dimension and $M$ is the number of clients. We rigorously prove that Fed-NGA is robust to both Byzantine faults and data heterogeneity. For non-convex loss functions, Fed-NGA achieves convergence to a neighborhood of stationary points under general assumptions, and further attains zero optimality gap under some mild conditions, which is an outcome rarely achieved in existing literature. In both cases, the convergence rate is $\mathcal{O}(1/T^{\frac{1}{2} - δ})$, where $T$ denotes the number of iterations and $δ\in (0, 1/2)$. Experimental results on benchmark datasets confirm the superior time efficiency and convergence performance of Fed-NGA over existing methods.

Xingrun Yan, Shiyuan Zuo, Rongfei Fan et al.

In a real federated learning (FL) system, communication overhead for passing model parameters between the clients and the parameter server (PS) is often a bottleneck. Hierarchical federated learning (HFL) that poses multiple edge servers (ESs) between clients and the PS can partially alleviate communication pressure but still needs the aggregation of model parameters from multiple ESs at the PS. To further reduce communication overhead, we bring sequential FL (SFL) into HFL for the first time, which removes the central PS and enables the model training to be completed only through passing the global model between two adjacent ESs for each iteration, and propose a novel algorithm adaptive to such a combinational framework, referred to as Fed-CHS. Convergence results are derived for strongly convex and non-convex loss functions under various data heterogeneity setups, which show comparable convergence performance with the algorithms for HFL or SFL solely. Experimental results provide evidence of the superiority of our proposed Fed-CHS on both communication overhead saving and test accuracy over baseline methods.

Shiyuan Zuo, Jiashuo Li, Rongfei Fan et al.

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 the theoretical lower bound required merely to read the gradients. We establish convergence guarantees under standard FL assumptions in prior Byzantine-robust FL analyses. By leveraging the Subspace Embedding Theorem, we show that PDR achieves optimal convergence rates of $ \mathcal{O}(1/\sqrt{T}) $ for non-convex functions and $ \mathcal{O}(1/T) $ for strongly convex functions, where $ T $ denotes the number of iterations. Crucially, we mathematically demonstrate that this massive acceleration comes almost for free, merely inflating the inherent Byzantine error floor by a bounded, tunable factor of $ \frac{1+ε}{1-ε} $. Experimental results on benchmark datasets confirm that integrating PDR with existing aggregators yields orders of magnitude speedups in time efficiency while maintaining highly competitive convergence performance.

Shiyuan Zuo, Xingrun Yan, Rongfei Fan et al.

This paper addresses federated learning (FL) in the context of malicious Byzantine attacks and data heterogeneity. We introduce a novel Robust Average Gradient Algorithm (RAGA), which uses the geometric median for aggregation and {allows flexible round number for local updates.} Unlike most existing resilient approaches, which base their convergence analysis on strongly-convex loss functions or homogeneously distributed datasets, this work conducts convergence analysis for both strongly-convex and non-convex loss functions over heterogeneous datasets. The theoretical analysis indicates that as long as the fraction of the {data} from malicious users is less than half, RAGA can achieve convergence at a rate of $\mathcal{O}({1}/{T^{2/3- δ}})$ for non-convex loss functions, where $T$ is the iteration number and $δ\in (0, 2/3)$. For strongly-convex loss functions, the convergence rate is linear. Furthermore, the stationary point or global optimal solution is shown to be attainable as data heterogeneity diminishes. Experimental results validate the robustness of RAGA against Byzantine attacks and demonstrate its superior convergence performance compared to baselines under varying intensities of Byzantine attacks on heterogeneous datasets.