  We study the problem of efficient PAC active learning of homogeneous linear
classifiers (halfspaces) in $\mathbb{R}^d$, where the goal is to learn a
halfspace with low error using as few label queries as possible. Under the
extra assumption that there is a $t$-sparse halfspace that performs well on the
data ($t \ll d$), we would like our active learning algorithm to be {\em
attribute efficient}, i.e. to have label requirements sublinear in $d$. In this
paper, we provide a computationally efficient algorithm that achieves this
goal. Under certain distributional assumptions on the data, our algorithm
achieves a label complexity of $O(t \cdot \mathrm{polylog}(d, \frac 1
\epsilon))$. In contrast, existing algorithms in this setting are either
computationally inefficient, or subject to label requirements polynomial in $d$
or $\frac 1 \epsilon$.
