  In Bayesian Optimization (BO) we study black-box function optimization with
noisy point evaluations and Bayesian priors. Convergence of BO can be greatly
sped up by batching, where multiple evaluations of the black-box function are
performed in a single round. The main difficulty in this setting is to propose
at the same time diverse and informative batches of evaluation points. In this
work, we introduce DPP-Batch Bayesian Optimization (DPP-BBO), a universal
framework for inducing batch diversity in sampling based BO by leveraging the
repulsive properties of Determinantal Point Processes (DPP) to naturally
diversify the batch sampling procedure. We illustrate this framework by
formulating DPP-Thompson Sampling (DPP-TS) as a variant of the popular Thompson
Sampling (TS) algorithm and introducing a Markov Chain Monte Carlo procedure to
sample from it. We then prove novel Bayesian simple regret bounds for both
classical batched TS as well as our counterpart DPP-TS, with the latter bound
being tighter. Our real-world, as well as synthetic, experiments demonstrate
improved performance of DPP-BBO over classical batching methods with Gaussian
process and Cox process models.
