Two gradient updates

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Problem

For $f(w)=(w-4)^2$ , start at $w_0=1$ with learning rate $\eta=\frac{1}{4}$ . Compute $w_1$ and $w_2$ .

Reveal answer or reference solution

The derivative is $f'(w)=2(w-4)$ . The first gradient is $-6$ , so

w_1=1-\frac{1}{4}(-6)=\frac{5}{2}.

The next gradient is $-3$ , so

w_2=\frac{5}{2}-\frac{1}{4}(-3)=\frac{13}{4}.

Both steps approach $w=4$ .

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Two gradient updates

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