A Distributed Synchronous SGD Algorithm with Global Top-$k$ Sparsification for Low Bandwidth Networks

Distributed synchronous stochastic gradient descent (S-SGD) with data parallelism requires very high communication bandwidth between computational workers (e.g., GPUs) to exchange gradients iteratively. Recently, Top-$k$ sparsification techniques have been proposed to reduce the volume of data to be exchanged among workers and thus alleviate the network pressure. Top-$k$ sparsification can zero-out a significant portion of gradients without impacting the model convergence. However, the sparse gradients should be transferred with their indices, and the irregular indices make the sparse gradients aggregation difficult. Current methods that use AllGather to accumulate the sparse gradients have a communication complexity of $O(kP)$, where $P$ is the number of workers, which is inefficient on low bandwidth networks with a large number of workers. We observe that not all Top-$k$ gradients from $P$ workers are needed for the model update, and therefore we propose a novel global Top-$k$ (gTop-$k$) sparsification mechanism to address the difficulty of aggregating sparse gradients. Specifically, we choose global Top-$k$ largest absolute values of gradients from $P$ workers, instead of accumulating all local Top-$k$ gradients to update the model in each iteration. The gradient aggregation method based on gTop-$k$ sparsification, namely gTopKAllReduce, reduces the communication complexity from $O(kP)$ to $O(klog_2P)$. Through extensive experiments on different DNNs, we verify that gTop-$k$ S-SGD has nearly consistent convergence performance with S-SGD. We evaluate the training efficiency of gTop-$k$ on a cluster with 32 GPU machines which are inter-connected with 1 Gbps Ethernet. The experimental results show that our method achieves up to $2.7-12\times$ higher scaling efficiency than S-SGD with dense gradients, and $1.1-1.7\times$ improvement than the existing Top-$k$ S-SGD.