We propose a Bayesian optimization algorithm for objective functions that are sums or integrals of expensive-to-evaluate functions, allowing noisy evaluations. These objective functions arise in multi-task Bayesian optimization for tuning machine learning hyperparameters, optimization via simulation, and sequential design of experiments with random environmental conditions. Our method is average-case optimal by construction when a single evaluation of the integrand remains within our evaluation budget. Achieving this one-step optimality requires solving a challenging value of information optimization problem, for which we provide a novel efficient discretization-free computational method. We also provide consistency proofs for our method in both continuum and discrete finite domains for objective functions that are sums. In numerical experiments comparing against previous state-of-the-art methods, including those that also leverage sum or integral structure, our method performs as well or better across a wide range of problems and offers significant improvements when evaluations are noisy or the integrand varies smoothly in the integrated variables.

提出一种用于贝叶斯优化的算法，优化对象为求和或积分形式、具有难以评估的函数，适用于机器学习超参数调优、模拟优化、随机实验设计等领域，该方法在单次函数评估处于预算内时具有平均情况最优性，通过解决信息价值优化问题达到了一步最优性，同时也在数值实验中表现优良。

昂贵积分的贝叶斯优化