Chang-Wei Shi

Chang-Wei Shi, Yi-Rui Yang, Wu-Jun Li

Distributed learning is essential for training large-scale deep models. Asynchronous SGD (ASGD) and its variants are commonly used distributed learning methods, particularly in scenarios where the computing capabilities of workers in the cluster are heterogeneous. Momentum has been acknowledged for its benefits in both optimization and generalization in deep model training. However, existing works have found that naively incorporating momentum into ASGD can impede the convergence. In this paper, we propose a novel method called ordered momentum (OrMo) for ASGD. In OrMo, momentum is incorporated into ASGD by organizing the gradients in order based on their iteration indexes. We theoretically prove the convergence of OrMo with both constant and delay-adaptive learning rates for non-convex problems. To the best of our knowledge, this is the first work to establish the convergence analysis of ASGD with momentum without dependence on the maximum delay. Empirical results demonstrate that OrMo can achieve better convergence performance compared with ASGD and other asynchronous methods with momentum.

Yi-Rui Yang, Chang-Wei Shi, Wu-Jun Li

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.

Shen-Yi Zhao, Chang-Wei Shi, Yin-Peng Xie et al.

Stochastic gradient descent~(SGD) and its variants have been the dominating optimization methods in machine learning. Compared to SGD with small-batch training, SGD with large-batch training can better utilize the computational power of current multi-core systems such as graphics processing units~(GPUs) and can reduce the number of communication rounds in distributed training settings. Thus, SGD with large-batch training has attracted considerable attention. However, existing empirical results showed that large-batch training typically leads to a drop in generalization accuracy. Hence, how to guarantee the generalization ability in large-batch training becomes a challenging task. In this paper, we propose a simple yet effective method, called stochastic normalized gradient descent with momentum~(SNGM), for large-batch training. We prove that with the same number of gradient computations, SNGM can adopt a larger batch size than momentum SGD~(MSGD), which is one of the most widely used variants of SGD, to converge to an $ε$-stationary point. Empirical results on deep learning verify that when adopting the same large batch size, SNGM can achieve better test accuracy than MSGD and other state-of-the-art large-batch training methods.

Chang-Wei Shi, Shen-Yi Zhao, Yin-Peng Xie et al.

With the rapid growth of data, distributed momentum stochastic gradient descent~(DMSGD) has been widely used in distributed learning, especially for training large-scale deep models. Due to the latency and limited bandwidth of the network, communication has become the bottleneck of distributed learning. Communication compression with sparsified gradient, abbreviated as \emph{sparse communication}, has been widely employed to reduce communication cost. All existing works about sparse communication in DMSGD employ local momentum, in which the momentum only accumulates stochastic gradients computed by each worker locally. In this paper, we propose a novel method, called \emph{\underline{g}}lobal \emph{\underline{m}}omentum \emph{\underline{c}}ompression~(GMC), for sparse communication. Different from existing works that utilize local momentum, GMC utilizes global momentum. Furthermore, to enhance the convergence performance when using more aggressive sparsification compressors (e.g., RBGS), we extend GMC to GMC+. We theoretically prove the convergence of GMC and GMC+. To the best of our knowledge, this is the first work that introduces global momentum for sparse communication in distributed learning. Empirical results demonstrate that, compared with the local momentum counterparts, our GMC and GMC+ can achieve higher test accuracy and exhibit faster convergence, especially under non-IID data distribution.