A Note on Reverse Pinsker Inequalities

TL;DR

This paper introduces a straightforward approach to derive optimal bounds on $f$-divergences, refining existing results and establishing their optimality under certain constraints on relative information extremums.

Contribution

It presents a simple method for obtaining optimal variational bounds on $f$-divergences, improving and generalizing known results with potential constraints.

Findings

Refined bounds on $f$-divergences.

Proved optimality of certain variational bounds.

Applicable under constraints on relative information extremums.

Abstract

A simple method is shown to provide optimal variational bounds on $f$-divergences with possible constraints on relative information extremums. Known results are refined or proved to be optimal as particular cases.