  Active search is a setting in adaptive experimental design where we aim to
uncover members of rare, valuable class(es) subject to a budget constraint. An
important consideration in this problem is diversity among the discovered
targets -- in many applications, diverse discoveries offer more insight and may
be preferable in downstream tasks. However, most existing active search
policies either assume that all targets belong to a common positive class or
encourage diversity via simple heuristics. We present a novel formulation of
active search with multiple target classes, characterized by a utility function
chosen from a flexible family whose members encourage diversity via a
diminishing returns mechanism. We then study this problem under the Bayesian
lens and prove a hardness result for approximating the optimal policy for
arbitrary positive, increasing, and concave utility functions. Finally, we
design an efficient, nonmyopic approximation to the optimal policy for this
class of utilities and demonstrate its superior empirical performance in a
variety of settings, including drug discovery.
