Gradient descent

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Consider the convex function $f(x) = 2(x - 3)^{2}$. Starting from $x_0 = -4$, take one step of gradient descent with learning rate $\eta = \frac{3}{10}$ using the update rule $x_1 = x_0 - \eta f'(x_0)$. Find $x_1$.

2. Warm-up

   Consider the convex function $f(x) = 4(x - 4)^{2}$. Starting from $x_0 = -6$, take one step of gradient descent with learning rate $\eta = \frac{1}{8}$ using the update rule $x_1 = x_0 - \eta f'(x_0)$. Find $x_1$.

3. Warm-up

   Consider the convex function $f(x) = 3(x - 2)^{2}$. Starting from $x_0 = -1$, take one step of gradient descent with learning rate $\eta = \frac{2}{10}$ using the update rule $x_1 = x_0 - \eta f'(x_0)$. Find $x_1$.

Problems shown under their original terms: Generated (template, solver-computed).