  Can one parallelize complex exploration exploitation tradeoffs? As an
example, consider the problem of optimal high-throughput experimental design,
where we wish to sequentially design batches of experiments in order to
simultaneously learn a surrogate function mapping stimulus to response and
identify the maximum of the function. We formalize the task as a multi-armed
bandit problem, where the unknown payoff function is sampled from a Gaussian
process (GP), and instead of a single arm, in each round we pull a batch of
several arms in parallel. We develop GP-BUCB, a principled algorithm for
choosing batches, based on the GP-UCB algorithm for sequential GP optimization.
We prove a surprising result; as compared to the sequential approach, the
cumulative regret of the parallel algorithm only increases by a constant factor
independent of the batch size B. Our results provide rigorous theoretical
support for exploiting parallelism in Bayesian global optimization. We
demonstrate the effectiveness of our approach on two real-world applications.
