Rényi分歧与优化
Rényi Divergence and Majorization
摘要：
雷尼发散与雷尼熵有关，就像信息发散（也称为Kullback-Leibler发散或相对熵）与香农熵有关一样，并且在许多情况下都会出现。它是由Rényi引入的，作为一种信息度量，满足与信息发散几乎相同的公理。我们回顾了Rényi散度的重要性质，包括它与其他距离的关系。我们展示了如何雷尼分歧出现时，控制理论是广义的从有限的连续设置。最后，雷尼发散在分析猜测随机变量序列的值所需的二进制问题的数量方面发挥了作用。
英文摘要：
Rényi divergence is related to Rényi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon's entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as information divergence. We review the most important properties of Rényi divergence, including its relation to some other distances. We show how Rényi divergence appears when the theory of majorization is generalized from the finite to the continuous setting. Finally, Rényi divergence plays a role in analyzing the number of binary questions required to guess the values of a sequence of random variables.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
