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.

💡 Research Summary

The paper challenges the widely held view that optimal biological behavior must be grounded in efficient information processing. To test this claim, the authors construct a minimal yet analytically tractable foraging model that captures a perception‑action loop: a creature moves on a one‑dimensional ring world while a single food source relocates stochastically along the same ring. The environment’s statistical structure is defined by the source’s transition probabilities, and the creature’s actions directly affect its future observations. The full system is represented as a Markov process on an infinite‑dimensional state space consisting of (creature position, source position, belief distribution). Because direct analysis of this space is infeasible, the authors introduce an exact coarse‑graining: they partition the raw states into a finite set of “information states” that share the same belief and decision rule. This reduction preserves the exact transition dynamics among information states, allowing the computation of steady‑state quantities such as average information gain (entropy reduction) and average utility (expected food collected per time step).

Three decision policies are examined. The first, an “information‑maximizing” strategy, selects actions that maximize the expected reduction in entropy of the belief about the source location at each step. The second, a “utility‑maximizing” strategy, directly maximizes the expected food intake by moving to the location with the highest posterior probability of containing the source. The third set includes simple baselines such as random wandering and a conservative policy that minimizes movement. For each policy the authors calculate (1) the long‑run average information gain, (2) the long‑run average utility, and (3) how the ranking of policies changes as a function of the source’s mobility parameter (the variance of its motion).

The results are striking. The information‑maximizing policy indeed yields the highest entropy reduction, yet its expected food intake is only intermediate, never surpassing the utility‑maximizing policy. Moreover, the ordering of policies by information performance does not predict their ordering by utility. In low‑mobility environments the conservative policy, which gathers little information, actually achieves the highest food collection because the source remains near its previous location. Conversely, when the source moves rapidly, the information‑seeking policy gains a relative advantage, though it still falls short of the utility‑maximizer. These findings demonstrate that maximizing information does not guarantee maximal expected utility, and that the relative benefit of any strategy depends critically on the statistical structure of the environment.

In the discussion the authors argue that while information theory has successfully explained many sensory and neural phenomena, it cannot serve as a universal explanatory principle for behavior. Information acquisition incurs costs (time, energy, missed feeding opportunities) that may outweigh its benefits, especially when the environment is predictable. Consequently, there is no simple monotonic relationship between information efficiency and behavioral optimality. The paper concludes that behavioral optimality does not imply information efficiency, nor is there a straightforward trade‑off between learning about a resource and exploiting it. This counterexample cautions against over‑generalizing information‑maximization principles to all aspects of biological decision‑making.