It is possible to define a regularizer to minimize

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rather than Formula $7\mathrm{.}5.$ How is this different than the existing regularizer? $[$Hint: Think about how this affects multiple datasets or for cross validation.$]$

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$-$fold cross validation, and then the model is learned for the whole dataset. How would the algorithm be different for the original way$($s$)$ of defining a regularizer and this alternative way? $[$Hint: There is a different number of examples used for the regularization than there is the full dataset; does this matter?$]$ Which works better in practice?