Design optimization under uncertainty is notoriously difficult when the objective function is expensive to evaluate. State-of-the-art techniques, e.g, stochastic optimization or sampling average approximation, fail to learn exploitable patterns from collected data and require an excessive number of objective function evaluations. There is a need for techniques that alleviate the high cost of information acquisition and select sequential simulations optimally. In the field of deterministic single-objective unconstrained global optimization, the Bayesian global optimization (BGO) approach has been relatively successful in addressing the information acquisition problem. BGO builds a probabilistic surrogate of the expensive objective function and uses it to define an information acquisition function (IAF) whose role is to quantify the merit of making new objective evaluations. Specifically, BGO iterates between making the observations with the largest expected IAF and rebuilding the probabilistic surrogate, until a convergence criterion is met. In this work, we extend the expected improvement (EI) IAF to the case of design optimization under uncertainty wherein the EI policy is reformulated to filter out parametric and measurement uncertainties. To increase the robustness of our approach in the low sample regime, we employ a fully Bayesian interpretation of Gaussian processes by constructing a particle approximation of the posterior of its hyperparameters using adaptive Markov chain Monte Carlo. We verify and validate our approach by solving two synthetic optimization problems under uncertainty and demonstrate it by solving the oil-well-placement problem with uncertainties in the permeability field and the oil price time series.
EXPObench: Benchmarking Surrogate-based Optimisation Algorithms on Expensive Black-box Functions
School of Industrial Engineering, Eindhoven University of Technology（埃因霍温理工大学工业工程学院）；Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology（代尔夫特理工大学电气工程、数学与计算机科学学院）
Robust Bayesian optimization with reinforcement learned acquisition functions
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Collaborative Innovation Center of Novel Software Technology and Industrialization（新型软件技术与产业化协同创新中心）；State Key Laboratory of Aerodynamics（空气动力学国家重点实验室）
