From c464d2fc6bdc81f9fa28c868fd1fca1987e6fa5b Mon Sep 17 00:00:00 2001 From: Stratis Ioannidis Date: Mon, 11 Feb 2013 17:19:34 -0800 Subject: math --- abstract.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'abstract.tex') diff --git a/abstract.tex b/abstract.tex index eebeb97..a92ad45 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 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{}. +We present a deterministic, polynomial time, truthful, budget feasible mechanism for \SEDP{}. 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. -- cgit v1.2.3-70-g09d2