Two Knobs, Two Steps, One Loss

A two-parameter model is trained on the loss

$L(w_1, w_2) = (2w_1 + w_2 - 7)^2 + 3w_2^{\,2}$

The second term is a penalty that pushes $w_2$ towards zero, so the two parameters are pulling against each other.

Both parameters are updated simultaneously. Within a single step, each partial derivative is evaluated at the parameter values held at the start of that step — before either parameter has moved:

$w_1 \leftarrow w_1 - \alpha\,\frac{\partial L}{\partial w_1}, \qquad w_2 \leftarrow w_2 - \alpha\,\frac{\partial L}{\partial w_2}$

quantity	value
starting $w_1$	$3$
starting $w_2$	$2$
learning rate $\alpha$	$0.05$
number of steps	$2$

What is the value of the loss after the two steps?

Round your answer to 2 decimal places.

Two Knobs, Two Steps, One Loss

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