  The Thresholding Bandit Problem (TBP) aims to find the set of arms with mean
rewards greater than a given threshold. We consider a new setting of TBP, where
in addition to pulling arms, one can also \emph{duel} two arms and get the arm
with a greater mean. In our motivating application from crowdsourcing, dueling
two arms can be more cost-effective and time-efficient than direct pulls. We
refer to this problem as TBP with Dueling Choices (TBP-DC). This paper provides
an algorithm called Rank-Search (RS) for solving TBP-DC by alternating between
ranking and binary search. We prove theoretical guarantees for RS, and also
give lower bounds to show the optimality of it. Experiments show that RS
outperforms previous baseline algorithms that only use pulls or duels.
