Title: Theoretical generalization bounds for improving the efficiency of deep online training. Abstract: In the era of data explosion, online machine learning in which learning models are updated in real-time has become essential due to the growth of data in practice. In particular, it is more challenging to collect and annotate new massive data accurately and timely compared to traditional offline supervised training settings. Although this online training framework has been shown to be practically beneficial, there has been a lack of theoretical guarantees for the learning performance, especially for the case with noisy labels. This paper aims to investigate a learning theory for both original deep online training and online training with noisy labels. We first introduce a theoretical bound of the gaps of empirical risks and gaps of generalization risks in micro-batch online training when learning with both clean and noisy labels. Those bounds will efficiently help guide the online training scheme when receiving new data. We next analyze the impact of micro-batch size on the learning performance of models with noisy labels through our experimental results on CIFAR10, and CIFAR100 datasets using different noise, which consistently demonstrates the merit of the bounds above in the online training setting.