With huge amounts of training data, deep learning has made great breakthroughs in many artificial intelligence (AI) applications. However, such large-scale data sets present computational challenges, requiring training to be distributed on a cluster equipped with accelerators like GPUs. With the fast increase of GPU computing power, the data communications among GPUs have become a potential bottleneck on the overall training performance. In this paper, we first propose a general directed acyclic graph (DAG) model to describe the distributed synchronous stochastic gradient descent (S-SGD) algorithm, which has been widely used in distributed deep learning frameworks. To understand the practical impact of data communications on training performance, we conduct extensive empirical studies on four state-of-the-art distributed deep learning frameworks (i.e., Caffe-MPI, CNTK, MXNet and TensorFlow) over multi-GPU and multi-node environments with different data communication techniques, including PCIe, NVLink, 10GbE, and InfiniBand. Through both analytical and experimental studies, we identify the potential bottlenecks and overheads that could be further optimized. At last, we make the data set of our experimental traces publicly available, which could be used to support simulation-based studies.
S-SGD requires the set of computing units (e.g., GPUs) to exchange data iteratively, which can be implemented by either parameter server (PS) based methods @cite_27 @cite_2 or decentralized methods. In PS-based methods, there is one or more PSes that store the global model. The PS aggregates parameters at each iteration, updates the model, and then pushes the updated model to each computing unit. Performance models have been built by S. @cite_30 to generalize the performance of the PS-based methods, which provides guidelines for better system scalability.
@cite_30 @cite_27 @cite_2
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Matrix factorization, when the matrix has missing values, has become one of the leading techniques for recommender systems. To handle web-scale datasets with millions of users and billions of ratings, scalability becomes an important issue. Alternating least squares (ALS) and stochastic gradient descent (SGD) are two popular approaches to compute matrix factorization, and there has been a recent flurry of activity to parallelize these algorithms. However, due to the cubic time complexity in the target rank, ALS is not scalable to large-scale datasets. On the other hand, SGD conducts efficient updates but usually suffers from slow convergence that is sensitive to the parameters. Coordinate descent, a classical optimization approach, has been used for many other large-scale problems, but its application to matrix factorization for recommender systems has not been thoroughly explored. In this paper, we show that coordinate descent-based methods have a more efficient update rule compared to ALS and have faster and more stable convergence than SGD. We study different update sequences and propose the CCD++ algorithm, which updates rank-one factors one by one. In addition, CCD++ can be easily parallelized on both multi-core and distributed systems. We empirically show that CCD++ is much faster than ALS and SGD in both settings. As an example, with a synthetic dataset containing 14.6 billion ratings, on a distributed memory cluster with 64 processors, to deliver the desired test RMSE, CCD++ is 49 times faster than SGD and 20 times faster than ALS. When the number of processors is increased to 256, CCD++ takes only 16 s and is still 40 times faster than SGD and 20 times faster than ALS. Matrix factorization, when the matrix has missing values, has become one of the leading techniques for recommender systems. To handle web-scale datasets with millions of users and billions of ratings, scalability becomes an important issue. Alternating Least Squares (ALS) and Stochastic Gradient Descent (SGD) are two popular approaches to compute matrix factorization. There has been a recent flurry of activity to parallelize these algorithms. However, due to the cubic time complexity in the target rank, ALS is not scalable to large-scale datasets. On the other hand, SGD conducts efficient updates but usually suffers from slow convergence that is sensitive to the parameters. Coordinate descent, a classical optimization approach, has been used for many other large-scale problems, but its application to matrix factorization for recommender systems has not been explored thoroughly. In this paper, we show that coordinate descent based methods have a more efficient update rule compared to ALS, and are faster and have more stable convergence than SGD. We study different update sequences and propose the CCD++ algorithm, which updatesrank-one factors one by one. In addition, CCD++ can be easily parallelized on both multi-core and distributed systems. We empirically show that CCD++ is much faster than ALS and SGD in both settings. As an example, on a synthetic dataset with 2 billion ratings, CCD++ is 4 times faster than both SGD and ALS using a distributed system with 20 machines. Synchronized stochastic gradient descent (SGD) optimizers with data parallelism are widely used in training large-scale deep neural networks. Although using larger mini-batch sizes can improve the system scalability by reducing the communication-to-computation ratio, it may hurt the generalization ability of the models. To this end, we build a highly scalable deep learning training system for dense GPU clusters with three main contributions: (1) We propose a mixed-precision training method that significantly improves the training throughput of a single GPU without losing accuracy. (2) We propose an optimization approach for extremely large mini-batch size (up to 64k) that can train CNN models on the ImageNet dataset without losing accuracy. (3) We propose highly optimized all-reduce algorithms that achieve up to 3x and 11x speedup on AlexNet and ResNet-50 respectively than NCCL-based training on a cluster with 1024 Tesla P40 GPUs. On training ResNet-50 with 90 epochs, the state-of-the-art GPU-based system with 1024 Tesla P100 GPUs spent 15 minutes and achieved 74.9 top-1 test accuracy, and another KNL-based system with 2048 Intel KNLs spent 20 minutes and achieved 75.4 accuracy. Our training system can achieve 75.8 top-1 test accuracy in only 6.6 minutes using 2048 Tesla P40 GPUs. When training AlexNet with 95 epochs, our system can achieve 58.7 top-1 test accuracy within 4 minutes, which also outperforms all other existing systems. We address the issue of using mini-batches in stochastic optimization of SVMs. We show that the same quantity, the spectral norm of the data, controls the parallelization speedup obtained for both primal stochastic subgradient descent (SGD) and stochastic dual coordinate ascent (SCDA) methods and use it to derive novel variants of mini-batched SDCA. Our guarantees for both methods are expressed in terms of the original nonsmooth primal problem based on the hinge-loss.