Optimal Mini-Batch Size Selection for Fast Gradient Descent
This work addresses a practical bottleneck in machine learning efficiency for researchers and practitioners, offering incremental improvements in training speed.
This paper tackles the problem of selecting mini-batch sizes to minimize Stochastic Gradient Descent (SGD) training time, revealing an empirical inverse law between batch size and update count and providing a closed-form model for training time optimization.
This paper presents a methodology for selecting the mini-batch size that minimizes Stochastic Gradient Descent (SGD) learning time for single and multiple learner problems. By decoupling algorithmic analysis issues from hardware and software implementation details, we reveal a robust empirical inverse law between mini-batch size and the average number of SGD updates required to converge to a specified error threshold. Combining this empirical inverse law with measured system performance, we create an accurate, closed-form model of average training time and show how this model can be used to identify quantifiable implications for both algorithmic and hardware aspects of machine learning. We demonstrate the inverse law empirically, on both image recognition (MNIST, CIFAR10 and CIFAR100) and machine translation (Europarl) tasks, and provide a theoretic justification via proving a novel bound on mini-batch SGD training.