Question 8: Consider an ML model for which the un-regularized loss on…

Consider an ML model for which the un-regularized loss on some dataset $D$ as a function of parameter vector $w = (w_1, w_2)$ is $L_D(w) = w_1^2 + w_2^2 - 2w_1 - 2w_2 + 2$. Let the L2- regularization term be $L_R(w) = \frac{\lambda}{2} \cdot ||w||^2$, where $\lambda > 0$ is the regularization rate. The L2-regularized total loss is $L = L_D + L_R$. Define:

$\begin{aligned} w_D^* &= \underset{w}{\arg\min}\ L_D \\ w^* &= \underset{w}{\arg\min}\ L \end{aligned}$

arg min returns the value of $w$ at which the function attains its minimum.

The subquestions are independent of each other.

Based on the above data, answer the given subquestions.