Information Acquisition Under Resource Limitations in a Noisy Environment
This addresses resource-limited decision-making in noisy environments, with implications for rational inattention and formula learning, but it is incremental as it builds on existing theoretical models.
The paper tackles the problem of an agent guessing the truth value of a Boolean formula under resource constraints and noisy tests, showing that finding an optimal strategy is generally hard but proposing a useful heuristic.
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 $\varphi$ 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.