Information Acquisition Under Resource Limitations in a Noisy Environment

We introduce a theoretical model of information acquisition under resource limitations in a noisy environment. An agent must guess the truth value of a given Boolean formula $φ$ after performing a bounded number of noisy tests of the truth values of variables in the formula. We observe that, in general, the problem of finding an optimal testing strategy for $ϕ$ is hard, but we suggest a useful heuristic. The techniques we use also give insight into two apparently unrelated, but well-studied problems: (1) \emph{rational inattention}, that is, when it is rational to ignore pertinent information (the optimal strategy may involve hardly ever testing variables that are clearly relevant to $ϕ$), and (2) what makes a formula hard to learn/remember.

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