Title: On Batch-size Selection for Stochastic Training for Graph Neural Networks. Abstract: Batch size is an important hyper-parameter for training deep learning models with stochastic gradient decent (SGD) method, and it has great influence on the training time and model performance. We study the batch size selection problem for training graph neural network (GNN) with SGD method. 
To reduce the training time while keeping a decent model performance, we propose a metric that combining both the variance of gradients and compute time for each mini-batch. We theoretically analyze how batch-size influence such a metric and propose the formula to evaluate some rough range of optimal batch size. 
In GNN, gradients evaluated on samples in a mini-batch are not independent and it is challenging to evaluate the exact variance of gradients. To address the dependency, we analyze an estimator for gradients that considers the randomness arising from two consecutive layers in GNN, and suggest a guideline for picking the appropriate scale of the batch size. 
We complement our theoretical results with extensive empirical experiments for ClusterGCN, FastGCN and GraphSAINT on 4 datasets: Ogbn-products, Ogbn-arxiv, Reddit and Pubmed. We demonstrate that in contrast to conventional deep learning models, GNNs benefit from large batch sizes.