Why is the term displacement not regularized in ridge regression?

In most classifications (e.g. logistic / linear regression), the term bias is ignored during regularization. Will we come to a better classification if we do not adjust the term bias?

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Example:

Y = aX + b

Regularization is based on the idea that redefinition is not Ydue to what ais "overly specific", so to speak, which is usually manifested by large values ​​of elements a.

b , . , - .

, : Y = aX + b, a , b .

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