  We propose a first-order stochastic optimization algorithm incorporating
adaptive regularization applicable to machine learning problems in deep
learning framework. The adaptive regularization is imposed by stochastic
process in determining batch size for each model parameter at each optimization
iteration. The stochastic batch size is determined by the update probability of
each parameter following a distribution of gradient norms in consideration of
their local and global properties in the neural network architecture where the
range of gradient norms may vary within and across layers. We empirically
demonstrate the effectiveness of our algorithm using an image classification
task based on conventional network models applied to commonly used benchmark
datasets. The quantitative evaluation indicates that our algorithm outperforms
the state-of-the-art optimization algorithms in generalization while providing
less sensitivity to the selection of batch size which often plays a critical
role in optimization, thus achieving more robustness to the selection of
regularity.
