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Batch size can be used for regularisation, but using it for that will limit training performance. From the Google Research Tuning Playbook:
> The batch size governs the training speed and shouldn't be used to directly tune the validation set performance. Often, the ideal batch size will be the largest batch size supported by the available hardware.
> […]
> As long as all hyperparameters are well-tuned (especially the learning rate and regularization hyperparameters) and the number of training steps is sufficient, the same final performance should be attainable using any batch size (see Shallue et al. 2018).
https://github.com/google-research/tuning_playbook#choosing-...
The ideal case is full-batch with tuneable regularisation, just the hardware gets expensive.