One Epoch, Two Mini-Batches

A one-parameter model $\hat{y} = w x$ (no intercept) is trained on six examples:

Training uses mini-batch gradient descent with a batch size of $3$. For a mini-batch $B$ containing $m$ examples, the loss and its gradient are

$J_B(w) = \frac{1}{m}\sum_{i \in B}\left(w x_i - y_i\right)^2, \qquad \frac{dJ_B}{dw} = \frac{2}{m}\sum_{i \in B}\left(w x_i - y_i\right)x_i$

One epoch consists of two updates taken in order:

• update 1 uses the mini-batch $\{(1,3),\;(2,5),\;(3,8)\}$;
• update 2 uses the mini-batch $\{(4,9),\;(5,12),\;(6,14)\}$, and its gradient is evaluated at the weight that update 1 has already produced — not at the starting weight.

Training starts at $w = 2$ with learning rate $\eta = 0.02$.

What is the value of $w$ after one complete epoch?

Round your answer to 2 decimal places.