Part of Proceedings of Machine Learning and Systems 1 (MLSys 2019)

*Siyuan Ma, Mikhail Belkin*

Modern machine learning models are typically trained using Stochastic Gradient Descent (SGD) on massively parallel computing resources such as GPUs. Increasing mini-batch size is a simple and direct way to utilize the parallel computing capacity. For small batch an increase in batch size results in the proportional reduction in the training time, a phenomenon known as {\it linear scaling}. However, increasing batch size beyond a certain value leads to no further improvement in training time. In this paper we develop the first analytical framework that extends linear scaling to match the parallel computing capacity of a resource. The framework is designed for a class of classical kernel machines. It automatically modifies a standard kernel machine to output a mathematically equivalent prediction function, yet allowing for extended linear scaling, i.e., higher effective parallelization and faster training time on given hardware. The resulting algorithms are accurate, principled and very fast. For example, using a single Titan Xp GPU, training on ImageNet with $1.3\times 10^6$ data points and $1000$ labels takes under an hour, while smaller datasets, such as MNIST, take seconds. As the parameters are chosen analytically, based on the theoretical bounds, little tuning beyond selecting the kernel and the kernel parameter is needed, further facilitating the practical use of these methods.

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