  We develop an algorithm for minimizing a function using $n$ batched function
value measurements at each of $T$ rounds by using classifiers to identify a
function's sublevel set. We show that sufficiently accurate classifiers can
achieve linear convergence rates, and show that the convergence rate is tied to
the difficulty of active learning sublevel sets. Further, we show that the
bootstrap is a computationally efficient approximation to the necessary
classification scheme.
  The end result is a computationally efficient derivative-free algorithm
requiring no tuning that consistently outperforms other approaches on
simulations, standard benchmarks, real-world DNA binding optimization, and
airfoil design problems whenever batched function queries are natural.
