How to calculate optimal batch size

From the recent Deep Learning book by Goodfellow et al., chapter 8:

Minibatch sizes are generally driven by the following factors:

• Larger batches provide a more accurate estimate of the gradient, but with less than linear returns.
• Multicore architectures are usually underutilized by extremely small batches. This motivates using some absolute minimum batch size, below which there is no reduction in the time to process a minibatch.
• If all examples in the batch are to be processed in parallel (as is typically the case), then the amount of memory scales with the batch size. For many hardware setups this is the limiting factor in batch size.
• Some kinds of hardware achieve better runtime with specific sizes of arrays. Especially when using GPUs, it is common for power of 2 batch sizes to offer better runtime. Typical power of 2 batch sizes range from 32 to 256, with 16 sometimes being attempted for large models.
• Small batches can offer a regularizing effect (Wilson and Martinez, 2003), perhaps due to the noise they add to the learning process. Generalization error is often best for a batch size of 1. Training with such a small batch size might require a small learning rate to maintain stability because of the high variance in the estimate of the gradient. The total runtime can be very high as a result of the need to make more steps, both because of the reduced learning rate and because it takes more steps to observe the entire training set.

Which in practice usually means "in powers of 2 and the larger the better, provided that the batch fits into your (GPU) memory".

You might want also to consult several good posts here in Stack Exchange:

• Tradeoff batch size vs. number of iterations to train a neural network
• Selection of Mini-batch Size for Neural Network Regression
• How large should the batch size be for stochastic gradient descent?

Just keep in mind that the paper by Keskar et al. 'On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima', quoted by several of the posts above, has received some objections by other respectable researchers of the deep learning community.

Hope this helps...

UPDATE (Dec 2017):

There is a new paper by Yoshua Bengio & team, Three Factors Influencing Minima in SGD (Nov 2017); it is worth reading in the sense that it reports new theoretical & experimental results on the interplay between learning rate and batch size.

UPDATE (Mar 2021):

Of interest here is also another paper from 2018, Revisiting Small Batch Training for Deep Neural Networks (h/t to Nicolas Gervais), which runs contrary to the larger the better advice; quoting from the abstract:

The best performance has been consistently obtained for mini-batch sizes between m=2 and m=32, which contrasts with recent work advocating the use of mini-batch sizes in the thousands.

You can estimate the largest batch size using:

Max batch size= available GPU memory bytes / 4 / (size of tensors + trainable parameters)

Use the summaries provided by pytorchsummary (pip install) or keras (builtin).

E.g.

from torchsummary import summary
summary(model)
.....
.....
================================================================
Total params: 1,127,495
Trainable params: 1,127,495
Non-trainable params: 0
----------------------------------------------------------------
Input size (MB): 0.02
Forward/backward pass size (MB): 13.93
Params size (MB): 4.30
Estimated Total Size (MB): 18.25
----------------------------------------------------------------

Each instance you put in the batch will require a full forward/backward pass in memory, your model you only need once. People seem to prefer batch sizes of powers of two, probably because of automatic layout optimization on the gpu.

Don't forget to linearly increase your learning rate when increasing the batch size.

Let's assume we have a Tesla P100 at hand with 16 GB memory.

(16000 - model_size) / (forward_back_ward_size)
(16000 - 4.3) / 18.25 = 1148.29
rounded to powers of 2 results in batch size 1024