关于移位Rényi散度的一个猜想的解决
Resolution of a Conjecture on Shifted R'enyi Divergence
AI总结：
本文证明了Altschuler与Chewi关于移位Rényi散度的猜想：q=1时成立（对应KL散度），q>1非退化时不成立。
AI中文摘要：
Altschuler与Chewi提出猜想：两个等协方差的各向同性高斯分布之间的次高斯Orlicz-Wasserstein移位Rényi散度，可通过均值的确定性移位达到，这将为其分析所消耗的移位预算提供精确闭式表达。本文证明，当q=1时该猜想成立，此时Rényi散度退化为Kullback-Leibler散度；而当q>1且处于非退化区间时，该猜想不成立。
英文摘要：
Altschuler and Chewi conjecture that the sub-Gaussian Orlicz--Wasserstein shifted Rényi divergence between two isotropic Gaussians of equal covariance is attained by a deterministic shift of the mean, which would give an exact closed form for the shift budget consumed by their analysis. In this note, we show that this conjecture is true when $q=1$, where the Rényi divergence degenerates to the Kullback--Leibler divergence, and false for every $q>1$ outside the degenerate regime.
