A penalty on the intercept

Why is an intercept usually excluded from ridge regularisation? What changes if you penalise it?

An intercept represents the baseline level rather than sensitivity to a feature. Penalising it shrinks the baseline toward zero, so changing the target's origin can alter substantive predictions. Exclude its entry from the penalty matrix, or centre features and target and restore the training target mean afterward. Penalising an intercept can be intentional if a zero-baseline prior is justified.