New Upper bounds for KL-divergence Based on Integral Norms

TL;DR

This paper introduces new upper bounds for KL-divergence using integral norms of density functions, linking convergence in KL-divergence to $L^1$ and $L^2$ norms, and applies these bounds to analyze the rate of the entropic CLT.

Contribution

It provides novel upper bounds for KL-divergence based on $L^1$, $L^2$, and $L^inity$ norms, connecting divergence convergence with density function norms and analyzing the entropic CLT rate.

Findings

KL-divergence bounds relate to $L^1$ and $L^2$ convergence

Convergence in KL-divergence is sandwiched between $L^1$ and $L^2$ convergence

Applied bounds to the rate theorem of the entropic conditional CLT

Abstract

In this paper, some new upper bounds for Kullback-Leibler divergence(KL-divergence) based on $L^1, L^2$ and $L^\infty$ norms of density functions are discussed. Our findings unveil that the convergence in KL-divergence sense sandwiches between the convergence of density functions in terms of $L^1$ and $L^2$ norms. Furthermore, we endeavor to apply our newly derived upper bounds to the analysis of the rate theorem of the entropic conditional central limit theorem.