We consider L2-approximation on weighted reproducing kernel Hilbert spaces
of functions depending on infinitely many variables. We focus on unrestricted
linear information, admitting evaluations of arbitrary continuous linear
functionals. We distinguish between ANOVA and non-ANOVA spaces, where, by ANOVA
spaces, we refer to function spaces whose norms are induced by an underlying
ANOVA function decomposition. In ANOVA spaces, we provide an optimal algorithm
to solve the approximation problem using linear information. We determine the
upper and lower error bounds on the polynomial convergence rate of n-th
minimal worst-case errors, which match if the weights decay regularly. For
non-ANOVA spaces, we also establish upper and lower error bounds. Our analysis
reveals that for weights with a regular and moderate decay behavior, the
convergence rate of n-th minimal errors is strictly higher in ANOVA than in
non-ANOVA spaces.Comment: Submitted to the MCQMC 2022 conference proceeding