Increasing Batch Size Improves Convergence of Stochastic Gradient Descent with Momentum
This work addresses convergence efficiency in deep neural network training, offering a practical optimization strategy that is incremental but supported by theoretical analysis.
The paper tackles the problem of optimizing convergence in stochastic gradient descent with momentum (SGDM) by showing that using an increasing batch size, rather than a constant one, minimizes the expectation of the full gradient norm and leads to faster convergence to stationary points, with numerical results supporting this improvement.
Stochastic gradient descent with momentum (SGDM), in which a momentum term is added to SGD, has been well studied in both theory and practice. The theoretical studies show that the settings of the learning rate and momentum weight affect the convergence of SGDM. Meanwhile, the practical studies have shown that the batch-size setting strongly affects the performance of SGDM. In this paper, we focus on mini-batch SGDM with a constant learning rate and constant momentum weight, which is frequently used to train deep neural networks. We show theoretically that using a constant batch size does not always minimize the expectation of the full gradient norm of the empirical loss in training a deep neural network, whereas using an increasing batch size definitely minimizes it; that is, an increasing batch size improves the convergence of mini-batch SGDM. We also provide numerical results supporting our analyses, indicating specifically that mini-batch SGDM with an increasing batch size converges to stationary points faster than with a constant batch size, while also reducing computational cost. Python implementations of the optimizers used in the numerical experiments are available at https://github.com/iiduka-researches/NSHB_increasing_batchsize_acml25/.