On the power of iid information for linear approximation

Abstract

This survey is concerned with the power of random information for approximation in the (deterministic) worst-case setting, with special emphasis on information consisting of functionals selected independently and identically distributed (iid) at random on a class of admissible information functionals. We present a general result based on a weighted least squares method and derive consequences for special cases. Improvements are available if the information is ``Gaussian'' or if we consider iid function values for Sobolev spaces. We include open questions to guide future research on the power of random information in the context of information-based complexity.