I have just learned about regularisation as an approach to control over-fitting, and I would like to incorporate the idea into a simple implementation of backpropagation and Multilayer perceptron (MLP) that I put together.
Currently to avoid over-fitting, I cross-validate and keep the network with best score so far on the validation set. This works OK, but adding regularisation would benefit me in that correct choice of the regularisation algorithm and parameter would make my network converge on a non-overfit model more systematically.
The formula I have for the update term (from Coursera ML course) is stated as a batch update e.g. for each weight, after summing all the applicable deltas for the whole training set from error propagation, an adjustment of
lambda * current_weight is added as well before the combined delta is subtracted at the end of the batch, where
lambda is the regularisation parameter.
My implementation of backpropagation uses per-item weight updates. I am concerned that I cannot just copy the batch approach, although it looks OK intuitively to me. Does a smaller regularisation term per item work just as well?
lambda * current_weight / N where N is size of training set - at first glance this looks reasonable. I could not find anything on the subject though, and I wonder if that is because regularisation does not work as well with a per-item update, or even goes under a different name or altered formula.