# Convex Cost of Information via Statistical Divergence

## TL;DR

This paper introduces a new class of convex information cost functions based on Rényi divergences, capturing the idea that balanced signals are less costly, and extends beyond traditional posterior-separable costs to align with recent experimental findings.

## Contribution

It provides an axiomatic characterization of convex information costs using mixture convexity and sub-additivity, leading to a novel divergence-based class of costs that generalize standard models.

## Key findings

- Cost functions expressed via Rényi divergences between signal distributions.
- Characterization of costs that favor balanced over extreme signals.
- Special cases include maximum and convex transformations of posterior-separable costs.

## Abstract

This paper characterizes convex information costs using an axiomatic approach. We employ mixture convexity and sub-additivity, which capture the idea that producing "balanced" outputs is less costly than producing ``extreme'' ones. Our analysis leads to a novel class of cost functions that can be expressed in terms of R\'enyi divergences between signal distributions across states. This representation allows for deviations from the standard posterior-separable cost, thereby accommodating recent experimental evidence. We also characterize two simpler special cases, which can be written as either the maximum or a convex transformation of posterior-separable costs.