One Mini-Batch Step on a Linear Model

A one-parameter linear model predicts $\hat{y} = wx$ . The loss on a single example is $\ell_i = (wx_i - y_i)^2$ , and the loss on a mini-batch $B$ is the average over that mini-batch:

$L_B(w) = \frac{1}{|B|}\sum_{i \in B} (wx_i - y_i)^2$

The full training set is:

example	$x_i$	$y_i$
1	$1$	$3$
2	$2$	$2$
3	$3$	$4$
4	$4$	$9$

Starting from $w = 1$ , one mini-batch step is taken with learning rate $\alpha = 0.1$ on the mini-batch $B = \{\text{example }1,\ \text{example }2\}$ .

What is $w$ after that single update?

One Mini-Batch Step on a Linear Model

Hints