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 multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.

翻译：科学和工程中的若干基础问题涉及未知高维（黑箱）函数的全局优化任务，该函数将一组可控变量映射为昂贵实验的输出结果。贝叶斯优化技术以较少的客观函数评估次数解决全局优化问题而著称，但在处理高维输出时性能下降。为克服这一核心维度挑战，本文提出一种基于随机先验的神经架构自助聚合集成深度学习框架，用于贝叶斯优化与序列决策。通过合理选择架构，我们证明该框架能近似设计变量与目标量之间的函数关系，即使目标量取值于高维向量空间乃至无穷维函数空间。在贝叶斯优化背景下，我们采用重参数化蒙特卡洛近似多点（并行）采集函数增强所提概率代理模型，并拓展方法以兼容黑箱约束与多保真度信息源。我们将所提框架与当前最优贝叶斯优化方法进行对比测试，在多项高维输出挑战性任务中展现出优越性能，包括涉及涡轮机械转子叶片形状优化的约束多保真度优化任务。