Constrained robust Bayesian optimization of expensive noisy black‐box functions with guaranteed regret bounds
Constrained robust Bayesian optimization of expensive noisy black‐box functions with guaranteed regret bounds
复制标题
对昂贵的嘈杂黑盒函数进行约束鲁棒贝叶斯优化，并保证后悔范围
DOI：
10.1002/aic.17857
复制
发表时间：
2022
期刊：
影响因子：
3.7
通讯作者：
Paulson, Joel A.
中科院分区：
文献类型：
--
作者：
Kudva, Akshay;Sorourifar, Farshud;Paulson, Joel A.
许多真实的设计问题涉及到昂贵的黑盒函数的优化。贝叶斯优化（BO）是一种很有前途的方法，用于解决这些具有挑战性的问题，使用概率代理模型系统地权衡开发和探索的设计空间。虽然BO通常应用于无约束问题，但最近已扩展到约束设置。然而，目前的约束BO方法，不能确定的解决方案，是不可避免的不确定性。在这篇文章中，我们提出了一个强大的约束BO方法，约束adversarially鲁棒贝叶斯优化（CARBO），解决了这一挑战，通过联合建模的影响，设计变量和未知函数的不确定性。使用精确的罚函数，我们建立了找到近全局鲁棒解所需的CARBO迭代次数的界限，并提供了严格的收敛性证明。CARBO的优点是证明了两个案例研究，包括一个非凸基准问题和一个现实的鼓泡塔反应器设计问题。
Many real‐world design problems involve optimization of expensive black‐box functions. Bayesian optimization (BO) is a promising approach for solving such challenging problems using probabilistic surrogate models to systematically tradeoff between exploitation and exploration of the design space. Although BO is often applied to unconstrained problems, it has recently been extended to the constrained setting. Current constrained BO methods, however, cannot identify solutions that are robust to unavoidable uncertainties. In this article, we propose a robust constrained BO method, constrained adversarially robust Bayesian optimization (CARBO), that addresses this challenge by jointly modeling the effect of the design variables and uncertainties on the unknown functions. Using exact penalty functions, we establish a bound on the number of CARBO iterations required to find a near‐global robust solution and provide a rigorous proof of convergence. The advantages of CARBO are demonstrated on two case studies including a non‐convex benchmark problem and a realistic bubble column reactor design problem.