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Practical results have shown that deep learning optimizers using smallconstant learning rates, hyperparameters close to one, and large batch sizescan find the model parameters of deep neural networks that minimize the lossfunctions. We first show theoretical evidence that the momentum method(Momentum) and adaptive moment estimation (Adam) perform well in the sense thatthe upper bound of the theoretical performance measure is small with a smallconstant learning rate, hyperparameters close to one, and a large batch size.Next, we show that there exists a batch size called the critical batch sizeminimizing the stochastic first-order oracle (SFO) complexity, which is thestochastic gradient computation cost, and that SFO complexity increases oncethe batch size exceeds the critical batch size. Finally, we provide numericalresults that support our theoretical results. That is, the numerical resultsindicate that Adam using a small constant learning rate, hyperparameters closeto one, and the critical batch size minimizing SFO complexity has fasterconvergence than Momentum and stochastic gradient descent (SGD).

Critical Bach Size Minimizes Stochastic First-Order Oracle Complexity of Deep Learning Optimizer using Hyperparameters Close to One