In the case I use regularized logistic regression to train perceptron model with threshold

, for regularized logistic regression it means that I have had soft-order constraint on

, however for perceptron model, as suggested in Exercise 4.6, it looks like soft-order constraint on

doesn't regularize perceptron model at all. Meanwhile in practice, I see that regularized logistic regression does regularize perceptron model and

Andrew Ng's online course also suggests that regularized logistic regression fights against overfitting on classification problems.

What did I miss here?

Thank you very much in advance.