Gradient descent on a quadratic

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Problem

For $f(w)=(w-3)^2$ , start at $w_0=0$ . Compute $w_1$ for learning rates $0.1$ and $1.1$ . Explain which update moves toward the minimizer and why overly large learning rates can diverge.

Reveal answer or reference solution

The gradient at $0$ is $-6$ . With $\eta=0.1$ , $w_1=0.6$ . With $\eta=1.1$ , $w_1=6.6$ , overshooting $3$ . For this quadratic, convergence requires $0<\eta<1$ ; larger steps amplify error.

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Appears in

Machine Learning Diagnostic
Gradient Descent Practice
Optimization Practice