#l0-regularization

L0-regularized least squares scores a weight vector by $f(w) = \lVert Xw - y \rVert_2^2 + \lambda \lVert w \rVert_0$, where $\lVert w \rVert_0$ counts the non-zero weights. Two candidates are $w^1 = (0.8,\ 0,\ 0.03,\ 0.1)$ with squared error 4.0 and $w^2 = (0,\ 0,\ 0.22,\ 0)$ with squared error 6.5. Above which value of $\lambda$ does $w^2$ get the better (lower) score?