  A multivariate ridge function is a function of the form $f(x) =
g(a^{\scriptscriptstyle T} x)$, where $g$ is univariate and $a \in
\mathbb{R}^d$. We show that the recovery of an unknown ridge function defined
on the hypercube $[-1,1]^d$ with Lipschitz-regular profile $g$ suffers from the
curse of dimensionality when the recovery error is measured in the
$L_\infty$-norm, even if we allow randomized algorithms. If a limited number of
components of $a$ is substantially larger than the others, then the curse of
dimensionality is not present and the problem is weakly tractable provided the
profile $g$ is sufficiently regular.
