Parallelizing Exploration-Exploitation Tradeoffs with Gaussian Process Bandit Optimization
This work addresses the challenge of efficient batch optimization in Bayesian global optimization, providing theoretical support for parallelism in applications like experimental design, though it is incremental as it builds on existing GP-UCB methods.
The paper tackles the problem of parallelizing exploration-exploitation tradeoffs in high-throughput experimental design by formalizing it as a multi-armed bandit problem with Gaussian processes, developing the GP-BUCB algorithm, and proving that cumulative regret increases only by a constant factor independent of batch size compared to sequential approaches.
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.