Gradient descent is run on
L(w)=5w2−20w+3L(w) = 5w^2 - 20w + 3L(w)=5w2−20w+3
starting from w0=6w_0 = 6w0=6, with the update w←w−αL′(w)w \leftarrow w - \alpha L'(w)w←w−αL′(w).
Find the learning rate α\alphaα that lands exactly on the minimum in a single step, and say what the run does instead if α=0.25\alpha = 0.25α=0.25 is used.
Select all that apply.
α=0.15\alpha = 0.15α=0.15; and at α=0.25\alpha = 0.25α=0.25 the iterates oscillate about the minimum but still converge to it.
α=0.1\alpha = 0.1α=0.1; and at α=0.25\alpha = 0.25α=0.25 the iterates oscillate about the minimum with growing swings, so the run diverges.
α=0.2\alpha = 0.2α=0.2; and at α=0.25\alpha = 0.25α=0.25 the iterates diverge steadily to the right, never crossing the minimum.
α=0.4\alpha = 0.4α=0.4; and at α=0.25\alpha = 0.25α=0.25 the iterates converge to the minimum from one side.