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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 definedon the hypercube $[-1,1]^d$ with Lipschitz-regular profile $g$ suffers from thecurse of dimensionality when the recovery error is measured in the$L_\infty$-norm, even if we allow randomized algorithms. If a limited number ofcomponents of $a$ is substantially larger than the others, then the curse ofdimensionality is not present and the problem is weakly tractable provided theprofile $g$ is sufficiently regular.

The recovery of ridge functions on the hypercube suffers from the curse of dimensionality