This paper studies Bayesian optimization with noise-free observations. We introduce new algorithms rooted in scattered data approximation that rely on a random exploration step to ensure that the fill-distance of query points decays at a near-optimal rate. Our algorithms retain the ease of implementation of the classical GP-UCB algorithm and satisfy cumulative regret bounds that nearly match those conjectured in arXiv:2002.05096, hence solving a COLT open problem. Furthermore, the new algorithms outperform GP-UCB and other popular Bayesian optimization strategies in several examples.

翻译：本文研究无噪声观测下的贝叶斯优化问题。我们提出了基于散乱数据逼近的新算法，该算法通过引入随机探索步骤，确保查询点的填充距离以近乎最优的速率衰减。所提算法既保留了经典GP-UCB算法的易于实现特性，又满足与arXiv:2002.05096中猜想结果近乎匹配的累积遗憾界，从而解决了COLT开放问题。此外，在多个实例中，新算法的性能优于GP-UCB及其他主流贝叶斯优化策略。