SGD is the widely adopted method to train CNN. Conceptually it approximates the population with a randomly sampled batch; then it evenly trains batches by conducting a gradient update on every batch in an epoch. In this paper, we demonstrate Sampling Bias, Intrinsic Image Difference and Fixed Cycle Pseudo Random Sampling differentiate batches in training, which then affect learning speeds on them. Because of this, the unbiased treatment of batches involved in SGD creates improper load balancing. To address this issue, we present Inconsistent Stochastic Gradient Descent (ISGD) to dynamically vary training effort according to learning statuses on batches. Specifically ISGD leverages techniques in Statistical Process Control to identify a undertrained batch. Once a batch is undertrained, ISGD solves a new subproblem, a chasing logic plus a conservative constraint, to accelerate the training on the batch while avoid drastic parameter changes. Extensive experiments on a variety of datasets demonstrate ISGD converges faster than SGD. In training AlexNet, ISGD is 21.05 faster than SGD to reach 56 top1 accuracy under the exactly same experiment setup. We also extend ISGD to work on multiGPU or heterogeneous distributed system based on data parallelism, enabling the batch size to be the key to scalability. Then we present the study of ISGD batch size to the learning rate, parallelism, synchronization cost, system saturation and scalability. We conclude the optimal ISGD batch size is machine dependent. Various experiments on a multiGPU system validate our claim. In particular, ISGD trains AlexNet to 56.3 top1 and 80.1 top5 accuracy in 11.5 hours with 4 NVIDIA TITAN X at the batch size of 1536.
@cite_20 adapts the learning rate to the parameters, performing larger updates for infrequent parameters, and smaller updates for frequent parameters. It accumulates the squared gradients in the denominator, which will drastically shrink the learning rate. Subsequently, and have been developed to resolve the issue. These adaptive learning rate approaches adjust the extent of parameter updates w.r.t the parameter's update frequency to increase the robustness of training, while ISGD adjusts the frequency of a batch's gradient updates w.r.t the loss to improve the training efficiency. From this perspective, ISGD is different from the adaptive learning rate approaches.
@cite_20
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We present a new family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perform more informative gradient-based learning. Metaphorically, the adaptation allows us to find needles in haystacks in the form of very predictive but rarely seen features. Our paradigm stems from recent advances in stochastic optimization and online learning which employ proximal functions to control the gradient steps of the algorithm. We describe and analyze an apparatus for adaptively modifying the proximal function, which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal function that can be chosen in hindsight. We give several efficient algorithms for empirical risk minimization problems with common and important regularization functions and domain constraints. We experimentally study our theoretical analysis and show that adaptive subgradient methods outperform state-of-the-art, yet non-adaptive, subgradient algorithms.