Training neural networks | Monte Carlo Methods

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Assume that we have a dataset D = {(x_1, y_1), ... , (x_n, y_n)}.

We want to train a neural network and update the weights with gradients computed on every mini-batch.

If we shuffle our mini-batches on every epoch, does the training process become a Monte Carlo method?

On Wikipedia, it is stated: Monte Carlo methods are computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle.

And I believe that the process becomes random if we shuffle the order of batches. Thus, the training algorithm becomes Monte Carlo. What do you think?