Extending Expected Improvement for High-dimensional Stochastic Optimization of Expensive Black-Box Functions
Extending Expected Improvement for High-dimensional Stochastic Optimization of Expensive Black-Box Functions
复制标题
扩展昂贵黑盒函数的高维随机优化的预期改进
DOI：
10.1115/1.4034104
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Jitesh H. Panchal
中科院分区：
文献类型：
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作者：
Piyush Pandita;Ilias Bilionis;Jitesh H. Panchal
当目标函数的计算代价很高时，不确定性条件下的设计优化是非常困难的。最先进的技术，例如，随机优化或采样平均近似，不能从收集的数据中学习可利用的模式，并且需要过多的目标函数评估。有必要的技术，减轻高成本的信息采集和选择最佳的顺序模拟。在确定性单目标无约束全局优化领域，贝叶斯全局优化（BGO）方法已经相对成功地解决了信息获取问题。BGO建立了一个昂贵的目标函数的概率代理，并使用它来定义一个信息获取函数（IAF），其作用是量化的优点，使新的客观评价。具体来说，BGO在进行具有最大预期IAF的观测和重建概率代理之间迭代，直到满足收敛标准。在这项工作中，我们扩展的预期改善（EI）IAF的情况下，设计优化的不确定性，其中EI政策重新制定，以过滤掉参数和测量的不确定性。为了增加我们的方法在低样本制度的鲁棒性，我们采用了完全贝叶斯解释高斯过程通过构建粒子近似的后验超参数使用自适应马尔可夫链蒙特卡罗。我们验证和验证我们的方法，通过解决两个不确定性下的综合优化问题，并证明它通过解决在渗透率场和石油价格时间序列的不确定性的油井布局问题。
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.