Risk-Aware Information Theory

Hamidou Tembine

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arXiv · 2606.22524

Risk-Aware Information Theory

Hamidou Tembine

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Abstract

We develop a risk-aware information theory by replacing expectation with expectiles, introducing expectile entropy, divergence, and mutual information. These quantities exhibit behaviors impossible under Shannon's risk-neutral framework, including negative divergence under risk-seeking regimes and a fundamental separation from classical mutual information. In multiuser systems, the framework naturally induces a mean-field-type game theory of information exchange, where achievable rate regions become endogenous to heterogeneous risk-sensitivity indices. Our results reveal that Shannon information alone cannot quantify the extreme risks driving advanced machine intelligence, establishing a foundation for risk-aware communication, learning, collective intelligence, and safe autonomous systems.

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Hamidou Tembine. 2026-06-21. Risk-Aware Information Theory. https://arxiv.org/abs/2606.22524

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