Asynchronous pipeline model parallelism with a “1F1B” (one forward, one backward) schedule generates little bubble overhead and always provides quite a high throughput. However, the “1F1B” schedule inevitably leads to weight inconsistency and weight staleness issues due to the cross-training of different mini-batches across GPUs. To simultaneously address these two problems, in this paper, we propose an optimizer-dependent weight prediction strategy (a.k.a PipeOptim) for asynchronous pipeline training. The key insight of our proposal is that we employ a weight prediction strategy in the forward pass to approximately ensure that each mini-batch uses consistent and staleness-free weights to compute the forward pass of the “1F1B” schedule. To be concrete, we first construct the weight prediction scheme based on the update rule of the used optimizer when training the deep neural network models. Then throughout the “1F1B” pipeline training, each mini-batch is mandated to execute weight prediction, subsequently employing the predicted weights to perform the forward pass. As a result, PipeOptim 1) inherits the advantage of the “1F1B” schedule and generates high throughput, and 2) can ensure effective parameter learning regardless of the type of the used optimizer. We conducted extensive experimental evaluations using nine different deep-learning models to verify the effectiveness of our proposal. The experiment results demonstrate that PipeOptim outperforms the other five popular pipeline approaches including GPipe, PipeDream, PipeDream-2BW, SpecTrain, and XPipe.

In this paper, we propose a general deep learning training framework XGrad which introduces weight prediction into the popular gradient-based optimizers to boost their convergence and generalization when training the deep neural network (DNN) models. In particular, ahead of each mini-batch training, the future weights are predicted according to the update rule of the used optimizer and are then applied to both the forward pass and backward propagation. In this way, during the whole training period, the optimizer always utilizes the gradients w.r.t. the future weights to update the DNN parameters, making the gradient-based optimizer achieve better convergence and generalization compared to the original optimizer without weight prediction. XGrad is rather straightforward to implement yet pretty effective in boosting the convergence of gradient-based optimizers and the accuracy of DNN models. Empirical results concerning five popular optimizers including SGD with momentum, Adam, AdamW, AdaBelief, and AdaM3 demonstrate the effectiveness of our proposal. The experimental results validate that XGrad can attain higher model accuracy than the baseline optimizers when training the DNN models.

Support vector machines (SVMs) have been recognized as a powerful tool to perform linear classification. When combined with the sparsity-inducing nonconvex penalty, SVMs can perform classification and variable selection simultaneously. However, the nonconvex penalized SVMs in general cannot be solved globally and efficiently due to their nondifferentiability, nonconvexity, and nonsmoothness. Existing solutions to the nonconvex penalized SVMs typically solve this problem in a serial fashion, which are unable to fully use the parallel computing power of modern multi-core machines. On the other hand, the fact that many real-world data are stored in a distributed manner urgently calls for a parallel and distributed solution to the nonconvex penalized SVMs. To circumvent this challenge, we propose an efficient alternating direction method of multipliers (ADMM) based algorithm that solves the nonconvex penalized SVMs in a parallel and distributed way. We design many useful techniques to decrease the computation and synchronization cost of the proposed parallel algorithm. The time complexity analysis demonstrates the low time complexity of the proposed parallel algorithm. Moreover, the convergence of the parallel algorithm is guaranteed. Experimental evaluations on four LIBSVM benchmark datasets demonstrate the efficiency of the proposed parallel algorithm.

In this paper, we revisit the convergence of the Heavy-ball method, and present improved convergence complexity results in the convex setting. We provide the first non-ergodic O(1/k) rate result of the Heavy-ball algorithm with constant step size for coercive objective functions. For objective functions satisfying a relaxed strongly convex condition, the linear convergence is established under weaker assumptions on the step size and inertial parameter than made in the existing literature. We extend our results to multi-block version of the algorithm with both the cyclic and stochastic update rules. In addition, our results can also be extended to decentralized optimization, where the ergodic analysis is not applicable.