Which Ball Touches the Line First? — hard Mixed: Norms & Regularization problem | Incognition

Which Ball Touches the Line First?

30 pts · 30 coins

Mixed: Norms & RegularizationHard

Which Ball Touches the Line First?

A model has two weights $w = (w_1, w_2)$ and exactly one training constraint, which every candidate solution must satisfy exactly:

$w_1 + 2w_2 = 4$

This leaves an entire line of perfect fits, so a regulariser must choose among them. Define three minimisers over that line:

$w^{(1)}$ minimises $\|w\|_1 = |w_1| + |w_2|$ (the Lasso penalty)
$w^{(2)}$ minimises $\|w\|_2 = \sqrt{w_1^2 + w_2^2}$ (the Ridge penalty)
$w^{(\infty)}$ minimises $\|w\|_\infty = \max(|w_1|, |w_2|)$

Which option gives all three minimisers correctly?

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