This survey is concerned with the power of random information for approximation in the (deterministic) worst-case setting, with special emphasis on information that is obtained independently and identically distributed (iid) from a given distribution on a class of admissible information. 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：本综述关注随机信息在（确定性）最坏情况设定下进行逼近的能力，特别强调从允许信息类中某给定分布独立同分布（iid）获取的信息。我们提出一个基于加权最小二乘法的通用结论，并推导其在特殊情况下的应用。若信息服从"高斯"分布，或针对Sobolev空间考虑iid函数值，则可获得改进。我们提出了若干开放性问题，以引导未来在信息复杂性背景下关于随机信息能力的研究。