From e83baf10783c1cc6b368df8247c4c87c64d4428f Mon Sep 17 00:00:00 2001 From: Stratis Ioannidis Date: Tue, 9 Jul 2013 09:40:42 -0700 Subject: abstract --- abstract.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/abstract.tex b/abstract.tex index dc663d8..9e99fcd 100644 --- a/abstract.tex +++ b/abstract.tex @@ -18,7 +18,7 @@ We initiate the study of budgeted mechanisms for experimental design. In this se 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 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 $\log\log\frac{B}{\epsilon\delta}$. +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 $\log\log\frac{B}{\epsilon\delta}$. 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. -- cgit v1.2.3-70-g09d2