  Active search is a learning paradigm for actively identifying as many members
of a given class as possible. A critical target scenario is high-throughput
screening for scientific discovery, such as drug or materials discovery. In
this paper, we approach this problem in Bayesian decision framework. We first
derive the Bayesian optimal policy under a natural utility, and establish a
theoretical hardness of active search, proving that the optimal policy can not
be approximated for any constant ratio. We also study the batch setting for the
first time, where a batch of $b>1$ points can be queried at each iteration. We
give an asymptotic lower bound, linear in batch size, on the adaptivity gap:
how much we could lose if we query $b$ points at a time for $t$ iterations,
instead of one point at a time for $bt$ iterations. We then introduce a novel
approach to nonmyopic approximations of the optimal policy that admits
efficient computation. Our proposed policy can automatically trade off
exploration and exploitation, without relying on any tuning parameters. We also
generalize our policy to batch setting, and propose two approaches to tackle
the combinatorial search challenge. We evaluate our proposed policies on a
large database of drug discovery and materials science. Results demonstrate the
superior performance of our proposed policy in both sequential and batch
setting; the nonmyopic behavior is also illustrated in various aspects.
