An Algorithm for Computing the Stratonovich's Value of Information

TL;DR

This paper introduces an algorithm to compute Stratonovich's value of information, extending the concept to various information leakage constraints, with convergence guarantees and practical computation methods.

Contribution

It develops an alternating optimization algorithm for VoI under general and specific information leakage constraints, including convergence analysis.

Findings

Algorithm successfully computes Stratonovich's VoI under multiple leakage constraints.

Convergence conditions for the optimization algorithm are established.

Provides practical methods for different types of information leakage measures.

Abstract

We propose an algorithm for computing Stratonovich's value of information (VoI) that can be regarded as an analogue of the distortion-rate function. We construct an alternating optimization algorithm for VoI under a general information leakage constraint and derive a convergence condition. Furthermore, we discuss algorithms for computing VoI under specific information leakage constraints, such as Shannon's mutual information (MI), $f$-leakage, Arimoto's MI, Sibson's MI, and Csiszar's MI.