Budget Feasible Mechanisms for Experimental Design

Understand

In the classical experimental design setting, an experimenter E has access to a population of $n$ potential experiment subjects $i\in \{1,...,n\}$, each associated with a vector of features $x_i\in R^d$.

• Conducting an experiment with subject $i$ reveals an unknown value $y_i\in R$ to E.
• E typically assumes some hypothetical relationship between $x_i$'s and $y_i$'s, e.g., $y_i \approx \beta x_i$, and estimates $\beta$ from experiments, e.g., through linear regression.
• As a proxy for various practical constraints, E may select only a subset of subjects on which to conduct the experiment.