A variational characterization of Rényi divergences
A variational characterization of Rényi divergences
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Rényi 散度的变分表征
DOI：
10.1109/isit.2017.8006657
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
V. Anantharam
中科院分区：
文献类型：
--
作者：
V. Anantharam
我们给出了任意可测空间上任意两个概率分布之间的Rényi发散的变分特征。作为推论，由Atar，Chowdhary和Dupuis推出的关于有界可测函数的指数积分的变分公式是关于Rényi发散的。然后，我们利用相对熵率得到了两个平稳的有限状态马氏链之间Rényi发散率的一个类似的变分特征。这使得Atar，Chowdhary和Dupuis的变分公式在定态有限状态马氏链的框架下类似。
We present a variational characterization of the Rényi divergences between any two probability distributions on an arbitrary measurable space, in terms of relative entropies. This yields as a corollary a recently developed variational formula, due to Atar, Chowdhary and Dupuis, for exponential integrals of bounded measurable functions in terms of Rényi divergences. We then develop a similar variational characterization of the Rényi divergence rates between two stationary finite state Markov chains in terms of relative entropy rates. This leads to an analog of the variational formula of Atar, Chowdhary and Dupuis in the framework of stationary finite state Markov chains.