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.

翻译：本综述关注信息在（确定性）最坏情况设定下对逼近问题的能力，特别关注由一类可容许信息泛函上独立同分布（iid）随机选取的函数泛函所构成的信息。我们提出一个基于加权最小二乘法的通用结果，并推导出在特殊情况下的推论。若信息为“高斯型”或考虑索博列夫空间的iid函数值，则可获得改进结果。我们提出了若干未解决问题，以引导未来关于信息复杂度框架下随机信息能力的研究。