  We study $(\epsilon, \delta)$-PAC best arm identification, where a
decision-maker must identify an $\epsilon$-optimal arm with probability at
least $1 - \delta$, while minimizing the number of arm pulls (samples). Most of
the work on this topic is in the sequential setting, where there is no
constraint on the time taken to identify such an arm; this allows the
decision-maker to pull one arm at a time. In this work, the decision-maker is
given a deadline of $T$ rounds, where, on each round, it can adaptively choose
which arms to pull and how many times to pull them; this distinguishes the
number of decisions made (i.e., time or number of rounds) from the number of
samples acquired (cost). Such situations occur in clinical trials, where one
may need to identify a promising treatment under a deadline while minimizing
the number of test subjects, or in simulation-based studies run on the cloud,
where we can elastically scale up or down the number of virtual machines to
conduct as many experiments as we wish, but need to pay for the resource-time
used. As the decision-maker can only make $T$ decisions, she may need to pull
some arms excessively relative to a sequential algorithm in order to perform
well on all possible problems. We formalize this added difficulty with two
hardness results that indicate that unlike sequential settings, the ability to
adapt to the problem difficulty is constrained by the finite deadline. We
propose Elastic Batch Racing (EBR), a novel algorithm for this setting and
bound its sample complexity, showing that EBR is optimal with respect to both
hardness results. We present simulations evaluating EBR in this setting, where
it outperforms baselines by several orders of magnitude.
