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Information Maximization Fails to Maximize Expected Utility in a Simple Foraging Model

Information theory has explained the organization of many biological phenomena, from the physiology of sensory receptive fields to the variability of certain DNA sequence ensembles. Some scholars have proposed that information should provide the central explanatory principle in biology, in the sense that any behavioral strategy that is optimal for an organism's survival must necessarily involve efficient information processing. We challenge this view by providing a counterexample. We present an analytically tractable model for a particular instance of a perception-action loop: a creature searching for a food source confined to a one-dimensional ring world. The model incorporates the statistical structure of the creature's world, the effects of the creature's actions on that structure, and the creature's strategic decision process. The model takes the form of a Markov process on an infinite dimensional state space. To analyze it we construct an exact coarse graining that reduces the model to a Markov process on a finite number of "information states". This technique allows us to make quantitative comparisons between the performance of an information-theoretically optimal strategy with other candidate strategies on a food gathering task. We find that: 1. Information optimal search does not necessarily optimize utility (expected food gain). 2. The rank ordering of search strategies by information performance does not predict their ordering by expected food obtained. 3. The relative advantage of different strategies depends on the statistical structure of the environment, in particular the variability of motion of the source. We conclude that there is no simple relationship between information and utility. Behavioral optimality does not imply information efficiency, nor is there a simple tradeoff between gaining information about a food source versus obtaining the food itself.