GATE 2026 DA Q.55: solution and answer

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)