  Gaussian Process bandit optimization has emerged as a powerful tool for
optimizing noisy black box functions. One example in machine learning is
hyper-parameter optimization where each evaluation of the target function
requires training a model which may involve days or even weeks of computation.
Most methods for this so-called "Bayesian optimization" only allow sequential
exploration of the parameter space. However, it is often desirable to propose
batches or sets of parameter values to explore simultaneously, especially when
there are large parallel processing facilities at our disposal. Batch methods
require modeling the interaction between the different evaluations in the
batch, which can be expensive in complex scenarios. In this paper, we propose a
new approach for parallelizing Bayesian optimization by modeling the diversity
of a batch via Determinantal point processes (DPPs) whose kernels are learned
automatically. This allows us to generalize a previous result as well as prove
better regret bounds based on DPP sampling. Our experiments on a variety of
synthetic and real-world robotics and hyper-parameter optimization tasks
indicate that our DPP-based methods, especially those based on DPP sampling,
outperform state-of-the-art methods.
