Information acquisition under resource limitations in a noisy environment

Abstract

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) rational inattention (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.