Information Acquisition Under Resource Limitations in a Noisy Environment

TL;DR

This paper presents a theoretical model for how an agent acquires information efficiently under resource constraints in noisy environments, with implications for rational inattention and formula learnability.

Contribution

It introduces a novel model for resource-limited information acquisition in noisy settings and offers heuristics and insights into related problems like rational inattention.

Findings

Optimal testing strategies are generally hard to compute.

Heuristics can be effective for strategy selection.

Insights into rational inattention and formula complexity.

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 $\varphi$ 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 $\phi$ 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 $\phi$), and (2) what makes a formula hard to learn/remember.