Bregman-divergence-based Arimoto-Blahut algorithm

TL;DR

This paper introduces a novel Bregman-divergence-based Arimoto-Blahut algorithm that eliminates the need for convex minimization in each iteration, applicable to classical and quantum rate-distortion problems.

Contribution

It generalizes the Arimoto-Blahut algorithm using Bregman divergence, enabling minimization-free iterations for rate-distortion theory.

Findings

The new algorithm simplifies computations in rate-distortion problems.

It successfully derives optimal conditional distributions in numerical experiments.

Applicable to both classical and quantum information scenarios.

Abstract

We generalize the generalized Arimoto-Blahut algorithm to a general function defined over Bregman-divergence system. In existing methods, when linear constraints are imposed, each iteration needs to solve a convex minimization. Exploiting our obtained algorithm, we propose a minimization-free-iteration algorithm. This algorithm can be applied to classical and quantum rate-distortion theory. We numerically apply our method to the derivation of the optimal conditional distribution in the rate-distortion theory.