Bayesian optimization usually assumes that a Bayesian prior is given.
However, the strong theoretical guarantees in Bayesian optimization are often
regrettably compromised in practice because of unknown parameters in the prior.
In this paper, we adopt a variant of empirical Bayes and show that, by
estimating the Gaussian process prior from offline data sampled from the same
prior and constructing unbiased estimators of the posterior, variants of both
GP-UCB and probability of improvement achieve a near-zero regret bound, which
decreases to a constant proportional to the observational noise as the number
of offline data and the number of online evaluations increase. Empirically, we
have verified our approach on challenging simulated robotic problems featuring
task and motion planning.Comment: Proceedings of the Thirty-second Conference on Neural Information
Processing Systems, 201
