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I'm a newbie to Machine Learning and I'm not very good at math. I have read Learning From Data - A Short Course and met this Exercise 4.6 on page 133:

We have seen both the hard-order constraint and the soft-order constraint. Which do you expect to be more useful for binary classification using the perceptron model? [Hint: $ sign(w^{T}x) = \> sign(\alpha w^{T}x) $ for any $ \alpha > 0 $.]

From the hint of the question, I have guessed the answer: Soft-order constraint does not actually "regularize" the perceptron model at all (I'm not sure if I used the right word here, what I mean is that soft-order constraint does not "reduce" the "complexity" of the hypothesis set of the perceptron model), and so the hard-order constraint is more useful for binary classification using the perceptron model.

However, if the above answer is correct, then I do not understand how regularized logistic regression regularize perceptron hypothesis set in the above binary classification task?

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