Many papers study multivariate problems for \(d\)-variate functions with finite \(d\), in particular polynomial and weak tractability. In the case of infinitely many variables, the problems are generally approximated by problems with \(d\)-variate functions with error \(\varepsilon\), \(\varepsilon\to 0\) as \(d\to\infty\). Usually the cost of the evaluation increases with \(d\). The authors consider the case of functions of infinitely (countably) many variables belonging to a suitable separable weighted Hilbert space and algorithms that use finitely many arbitrary linear functionals. They provide an algorithm whose cost is minimal among all algorithms with error at most \(\varepsilon\) and show that this algorithm does not depend on the cost function. They also give necessary and sufficient conditions for the polynomial and weak tractability.