A conversion between utility and information

TL;DR

This paper establishes a theoretical link between utility and information content, showing that rewards can be uniquely derived from negative information content, and applies this to analyze agent-environment interactions through entropy measures.

Contribution

It introduces a novel information-theoretic framework for defining rewards based on negative information content and applies it to analyze stochastic processes and agent-environment systems.

Findings

Rewards are uniquely determined by negative information content.

Expected utility of a stochastic process equals its negative entropy rate.

Agent utility corresponds to negative cross-entropy between system and agent distributions.

Abstract

Rewards typically express desirabilities or preferences over a set of alternatives. Here we propose that rewards can be defined for any probability distribution based on three desiderata, namely that rewards should be real-valued, additive and order-preserving, where the latter implies that more probable events should also be more desirable. Our main result states that rewards are then uniquely determined by the negative information content. To analyze stochastic processes, we define the utility of a realization as its reward rate. Under this interpretation, we show that the expected utility of a stochastic process is its negative entropy rate. Furthermore, we apply our results to analyze agent-environment interactions. We show that the expected utility that will actually be achieved by the agent is given by the negative cross-entropy from the input-output (I/O) distribution of the coupled interaction system and the agent's I/O distribution. Thus, our results allow for an information-theoretic interpretation of the notion of utility and the characterization of agent-environment interactions in terms of entropy dynamics.