标题： 未知高斯过程先验的元贝叶斯优化的遗憾界 显示英文标题

标题： Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior

摘要： 贝叶斯优化通常假设一个贝叶斯先验已经给定。然而，由于先验中的未知参数，在实践中贝叶斯优化的强理论保证往往令人遗憾地被妥协。本文中，我们采用了一种经验贝叶斯的变体，并证明了通过从与先验相同的先验中采样的离线数据估计高斯过程先验并构建后验的无偏估计量，GP-UCB 和概率提升的变体都实现了接近零的遗憾界，该界随着离线数据的数量和在线评估次数的增加而减少到与观测噪声成比例的常数。在实验方面，我们在具有任务和运动规划的挑战性模拟机器人问题上验证了我们的方法。 显示英文摘要

摘要： 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.