Conservative Surrogate Models for Optimization with the Active Subspace Method
Philippe-André Luneau
我们有兴趣建立低维替代模型,以降低优化成本,同时通过保守近似,理论上保证最佳模型将满足全尺寸模型的限制。 替代模型使用高斯过程回归(GPR)构建。 为了确保保守,提出了两种新方法:第一个使用bootstrapping,第二个使用集中不等式。 这两种技术基于随机论证,因此只会强制保守到用户定义的概率阈值。 该方法在优化中使用主动子空间方法进行应用,以减小目标函数的尺寸和约束,解决有关约束违规的有记录问题。 生成的算法在热设计中的玩具优化问题上进行了测试。
We are interested in building low-dimensional surrogate models to reduce optimization costs, while having theoretical guarantees that the optimum will satisfy the constraints of the full-size model, by making conservative approximations. The surrogate model is constructed using a Gaussian process regression (GPR). To ensure conservativeness, two new approaches are proposed: the first one using bootstrapping, and the second one using concentration inequalities. Those two techniques are based on a...