标题： 高维昂贵黑箱函数的期望改进扩展方法 显示英文标题

标题： Extending Expected Improvement for High-dimensional Stochastic Optimization of Expensive Black-Box Functions

摘要： 在目标函数评估成本高昂的情况下，不确定性下的设计优化以著称的困难。 最先进的技术，例如随机优化或抽样平均逼近，在从收集的数据中学习可利用的模式方面失败，并且需要过多的目标函数评估次数。 需要能够减轻信息获取高成本并最优选择顺序模拟的技术。 在确定性单目标无约束全局优化领域，贝叶斯全局优化（BGO）方法在解决信息获取问题方面相对成功。 BGO构建了一个昂贵目标函数的概率代理模型，并使用它来定义一个信息获取函数（IAF），其作用是量化进行新目标评估的价值。 具体来说，BGO在进行具有最大期望IAF的观测和重建概率代理模型之间迭代，直到满足收敛准则。 在这项工作中，我们将期望改进（EI）IAF扩展到不确定性下的设计优化情况，其中EI策略被重新制定以过滤参数和测量不确定性。 为了在小样本情况下提高我们方法的鲁棒性，我们通过使用自适应马尔可夫链蒙特卡罗构建其超参数后验的粒子近似，采用高斯过程的完全贝叶斯解释。 我们通过解决两个合成的不确定性优化问题来验证和验证我们的方法，并通过解决具有渗透率场和石油价格时间序列不确定性的油井布置问题来展示它。 显示英文摘要

摘要： 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.