Convex Cost of Information via Statistical Divergence

Davide Bordoli and Ryota Iijima

Papers from arXiv.org

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.

Date: 2025-08
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