Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained optimization task involving shape optimization of rotor blades in turbo-machinery.

翻译：科学与工程领域的若干基础问题涉及未知高维（黑箱）函数的全局优化任务，此类函数将一组可控变量映射为昂贵实验的输出结果。贝叶斯优化技术凭借较少的函数评估次数即可有效解决全局优化问题，但在处理高维输出时性能显著下降。为攻克这一维度困境，本文提出一种基于随机先验引导的神经网络自助集成深度学习框架，用于贝叶斯优化与序列决策。通过合理的架构选择，我们证明该框架能够近似刻画设计变量与目标量之间的函数关系，即便目标量取值于高维向量空间甚至无限维函数空间。在贝叶斯优化场景下，我们将提出的概率代理模型与多点（并行）采集函数的重参数化蒙特卡洛近似结合，并拓展了处理黑箱约束与多保真信息源的方法论。我们针对先进的贝叶斯优化方法开展对比测试，在多项高维输出挑战性任务中展现了更优性能，其中包含透平机械转子叶片气动外形优化的约束优化问题。