On the Optimal Batch Size for Byzantine-Robust Distributed Learning

Byzantine-robust distributed learning (BRDL), in which computing devices are likely to behave abnormally due to accidental failures or malicious attacks, has recently become a hot research topic. However, even in the independent and identically distributed (i.i.d.) case, existing BRDL methods will suffer from a significant drop on model accuracy due to the large variance of stochastic gradients. Increasing batch sizes is a simple yet effective way to reduce the variance. However, when the total number of gradient computation is fixed, a too-large batch size will lead to a too-small iteration number (update number), which may also degrade the model accuracy. In view of this challenge, we mainly study the optimal batch size when the total number of gradient computation is fixed in this work. In particular, we theoretically and empirically show that when the total number of gradient computation is fixed, the optimal batch size in BRDL increases with the fraction of Byzantine workers. Therefore, compared to the case without attacks, the batch size should be set larger when under Byzantine attacks. However, for existing BRDL methods, large batch sizes will lead to a drop on model accuracy, even if there is no Byzantine attack. To deal with this problem, we propose a novel BRDL method, called Byzantine-robust stochastic gradient descent with normalized momentum (ByzSGDnm), which can alleviate the drop on model accuracy in large-batch cases. Moreover, we theoretically prove the convergence of ByzSGDnm for general non-convex cases under Byzantine attacks. Empirical results show that ByzSGDnm has a comparable performance to existing BRDL methods under bit-flipping failure, but can outperform existing BRDL methods under deliberately crafted attacks.

FedREP: A Byzantine-Robust, Communication-Efficient and Privacy-Preserving Framework for Federated Learning

Federated learning (FL) has recently become a hot research topic, in which Byzantine robustness, communication efficiency and privacy preservation are three important aspects. However, the tension among these three aspects makes it hard to simultaneously take all of them into account. In view of this challenge, we theoretically analyze the conditions that a communication compression method should satisfy to be compatible with existing Byzantine-robust methods and privacy-preserving methods. Motivated by the analysis results, we propose a novel communication compression method called consensus sparsification (ConSpar). To the best of our knowledge, ConSpar is the first communication compression method that is designed to be compatible with both Byzantine-robust methods and privacy-preserving methods. Based on ConSpar, we further propose a novel FL framework called FedREP, which is Byzantine-robust, communication-efficient and privacy-preserving. We theoretically prove the Byzantine robustness and the convergence of FedREP. Empirical results show that FedREP can significantly outperform communication-efficient privacy-preserving baselines. Furthermore, compared with Byzantine-robust communication-efficient baselines, FedREP can achieve comparable accuracy with the extra advantage of privacy preservation.

BASGD: Buffered Asynchronous SGD for Byzantine Learning

Distributed learning has become a hot research topic, due to its wide application in cluster-based large-scale learning, federated learning, edge computing and so on. Most distributed learning methods assume no error and attack on the workers. However, many unexpected cases, such as communication error and even malicious attack, may happen in real applications. Hence, Byzantine learning (BL), which refers to distributed learning with attack or error, has recently attracted much attention. Most existing BL methods are synchronous, which will result in slow convergence when there exist heterogeneous workers. Furthermore, in some applications like federated learning and edge computing, synchronization cannot even be performed most of the time due to the online workers (clients or edge servers). Hence, asynchronous BL (ABL) is more general and practical than synchronous BL (SBL). To the best of our knowledge, there exist only two ABL methods. One of them cannot resist malicious attack. The other needs to store some training instances on the server, which has the privacy leak problem. In this paper, we propose a novel method, called buffered asynchronous stochastic gradient descent (BASGD), for BL. BASGD is an asynchronous method. Furthermore, BASGD has no need to store any training instances on the server, and hence can preserve privacy in ABL. BASGD is theoretically proved to have the ability of resisting against error and malicious attack. Moreover, BASGD has a similar theoretical convergence rate to that of vanilla asynchronous SGD (ASGD), with an extra constant variance. Empirical results show that BASGD can significantly outperform vanilla ASGD and other ABL baselines, when there exists error or attack on workers.