From c60b7918b8a69ea362da3a58e239ef089e7e358a Mon Sep 17 00:00:00 2001
From: Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>
Date: Mon, 8 Jul 2013 14:02:27 -0700
Subject: eps

---
 abstract.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'abstract.tex')

diff --git a/abstract.tex b/abstract.tex
index 614a36b..dc663d8 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 constant 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 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. 
 
 
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