  We study exploration in stochastic multi-armed bandits when we have access to
a divisible resource that can be allocated in varying amounts to arm pulls. We
focus in particular on the allocation of distributed computing resources, where
we may obtain results faster by allocating more resources per pull, but might
have reduced throughput due to nonlinear scaling. For example, in
simulation-based scientific studies, an expensive simulation can be sped up by
running it on multiple cores. This speed-up however, is partly offset by the
communication among cores, which results in lower throughput than if fewer
cores were allocated per trial to run more trials in parallel. In this paper,
we explore these trade-offs in two settings. First, in a fixed confidence
setting, we need to find the best arm with a given target success probability
as quickly as possible. We propose an algorithm which trades off between
information accumulation and throughput and show that the time taken can be
upper bounded by the solution of a dynamic program whose inputs are the gaps
between the sub-optimal and optimal arms. We also prove a matching hardness
result. Second, we present an algorithm for a fixed deadline setting, where we
are given a time deadline and need to maximize the probability of finding the
best arm. We corroborate our theoretical insights with simulation experiments
that show that the algorithms consistently match or outperform baseline
algorithms on a variety of problem instances.
