diff options
Diffstat (limited to 'abstract.tex')
| -rwxr-xr-x | abstract.tex | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/abstract.tex b/abstract.tex index 9e99fcd..4cff1cd 100755 --- a/abstract.tex +++ b/abstract.tex @@ -1,5 +1,5 @@ %We initiate the study of mechanisms for \emph{experimental design}. - +\begin{comment} In the classical {\em experimental design} setting, an experimenter \E\ %with a budget $B$ @@ -17,8 +17,8 @@ As a proxy for various practical constraints, \E{} may select only a subset of s We initiate the study of budgeted mechanisms for experimental design. In this setting, \E{} has a budget $B$. Each subject $i$ declares an associated cost $c_i >0$ to be part of the experiment, and must be paid at least her cost. In particular, the {\em Experimental Design Problem} (\SEDP) is to find 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. Further, the subjects are \emph{strategic} and may lie about their costs. Thus, we need to design a mechanism for \SEDP{} with suitable properties. - -We present a deterministic, polynomial time, budget feasible mechanism scheme, that is approximately truthful and yields a constant ($\approx 12.98$) factor approximation to \EDP. %In particular, for any small $\delta>0$ and $\varepsilon>0$, we can construct a $(12.98\,,\varepsilon)$-approximate mechanism that is $\delta$-truthful and runs in polynomial time in both $n$ and $\log\log\frac{B}{\epsilon\delta}$. +\end{comment} +We present a deterministic, polynomial time, budget feasible mechanism scheme, that is approximately truthful and yields a constant ($\approx 12.98$) factor approximation for the \emph{Experimental Design Problem} (\EDP). %In particular, for any small $\delta>0$ and $\varepsilon>0$, we can construct a $(12.98\,,\varepsilon)$-approximate mechanism that is $\delta$-truthful and runs in polynomial time in both $n$ and $\log\log\frac{B}{\epsilon\delta}$. By applying previous work on budget feasible mechanisms with a submodular objective, one could {\em only} have derived either an exponential time deterministic mechanism or a randomized polynomial time mechanism. We also establish that no truthful, budget-feasible mechanism is possible within a factor $2$ approximation, and show how to generalize our approach to a wide class of learning problems, beyond linear regression. |