Information Theory

Remarks on reverse Pinsker inequalities

X. Y. Gui^a, Y. C. Huang<sup>bc

a</sup> School of Transportation Engineering, East China Jiaotong University, Nanchang, Jiangxi Province, People’s Republic of China
^b Institut Galilée, LAGA, CNRS (UMR 7539), Université Sorbonne Paris Nord, Villetaneuse, France
^c School of Mathematical Sciences, Nanjing Normal University, Nanjing, People’s Republic of China

Abstract: In this note we propose a simplified approach to recent reverse Pinsker inequalities due to O. Binette. More precisely, we give direct proofs of optimal variational bounds on $f$-divergence with possible constraints on relative information extrema. Our arguments are closer in spirit to those of Sason and Verdú.

Keywords: Kullback–Leibler divergence, total variation, reverse Pinsker inequalities, $f$-divergence, convexity, sharp inequalities, extremizer.

UDC: 621.391 : 519.72

Received: 24.06.2022
Revised: 23.09.2022
Accepted: 24.09.2022

DOI: 10.31857/S0555292322040015

 English version: Problems of Information Transmission, 2022, 58:4, 297–299