  We initiate the study of active learning polynomial threshold functions
(PTFs). While traditional lower bounds imply that even univariate quadratics
cannot be non-trivially actively learned, we show that allowing the learner
basic access to the derivatives of the underlying classifier circumvents this
issue and leads to a computationally efficient algorithm for active learning
degree-$d$ univariate PTFs in $\tilde{O}(d^3\log(1/\varepsilon\delta))$
queries. We also provide near-optimal algorithms and analyses for active
learning PTFs in several average case settings. Finally, we prove that access
to derivatives is insufficient for active learning multivariate PTFs, even
those of just two variables.
