GATE DA 2026 Q55: Regularised loss for one ridge regression example

Consider that Linear Ridge Regression is being used to learn a prediction function $y_{pred} = w^T x$, where $w, x \in \mathbb{R}^2$ and Mean Absolute Error (MAE) is used to measure the prediction error. A weight of 0.20 is associated with the regularizer.

At an intermediate step of the training process, assume that the parameter $w = [-3.00, 4.00]^T$. In the next step, for the input $x = [1.00, 2.00]^T$, the predicted value of $y$ is noted. Let the relation between $x = [x_1, x_2]^T$ and the true value of $y$ be $y_{true} = x_1 + x_2$.

The value of the overall regularized loss function for this instance is _______. (Rounded off to two decimal places)