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diff --git a/abstract.tex b/abstract.tex index f005dbf..eebeb97 100644 --- a/abstract.tex +++ b/abstract.tex @@ -1,21 +1,24 @@ %We initiate the study of mechanisms for \emph{experimental design}. In the classical {\em experimental design} setting, -an experimenter \E\ with a budget $B$ has access to a population of $n$ potential experiment subjects $i\in \{1,\ldots,n\}$, each associated with a vector of features $x_i\in\reals^d$ as well as a cost $c_i>0$. +an experimenter \E\ +%with a budget $B$ +has access to a population of $n$ potential experiment subjects $i\in \{1,\ldots,n\}$, each associated with a vector of features $x_i\in\reals^d$. +%as well as a cost $c_i>0$. Conducting an experiment with subject $i$ reveals an unknown value $y_i\in \reals$ to \E. \E\ typically assumes some hypothetical relationship between $x_i$'s and $y_i$'s, \emph{e.g.}, $y_i \approx \T{\beta} x_i$, and estimates $\beta$ from experiments. %conducting the experiments and obtaining the measurements $y_i$ allows %\E\ can estimate $\beta$. -\E 's goal is to select which experiments to conduct, subject to her budget constraint. +As a proxy for various practical constraints, \E{} may select subjects to select for the experiments. +%\E 's goal is to select which experiments to conduct, subject to her budget constraint. %, to obtain the best estimate possible for $\beta$. -We initiate the study of mechanisms for experimental design. In this setting, -subjects are \emph{strategic} and may lie about their costs. In particular, we formulate the {\em Experimental Design Problem} (\EDP) as finding a set $S$ of subjects that maximize $V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i})$ under the constraint $\sum_{i\in S}c_i\leq B$; our objective function corresponds to the information gain in $\beta$ when it is learned through linear regression methods, and is related to the so-called $D$-optimality criterion. We present the first known -deterministic, polynomial time, truthful, budget feasible mechanism for \EDP{}. -Our mechanism yields a constant factor ($\approx 19.68$) approximation, and we show that no truthful, budget-feasible algorithms are possible within a factor 2 approximation. -Our approach here generally applies to a wider class of learning problems and -obtains polynomial time universally truthful (\emph{i.e.}, randomized) budget feasible mechanism, also within a constant factor approximation. +We initiate the study of budgeted mechanisms for experimental design. In this setting, \E{} has a budget $B$. +Each subject $i$ declares associated cost $c_i >0$ to be part of the experiment, and must be paid at least their cost. Further, the subjects +are \emph{strategic} and may lie about their costs . In particular, we formulate the {\em Strategic Experimental Design Problem} (\SEDP) as finding a set $S$ of subjects for the experiment that maximizes $V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i})$ under the constraint $\sum_{i\in S}c_i\leq B$; our objective function corresponds to the information gain in parameter $\beta$ that is learned through linear regression methods, and is related to the so-called $D$-optimality criterion. +We present a deterministic, polynomial time, truthful, budget feasible mechanism for \EDP{}. +By applying previous work on budget feasible mechanisms with submodular objective, one could have derived either an exponential time deterministic mechanism or a randomized polynomial time mechanism. Our mechanism yields a constant factor ($\approx 12.68$) approximation, and we show that no truthful, budget-feasible algorithms are possible within a factor $2$ approximation. We also show how to apply our approach to a wide class of learning problems. |