Adaptive batching for Gaussian process surrogates with application in noisy level set estimation
Adaptive batching for Gaussian process surrogates with application in noisy level set estimation
复制标题
DOI：
10.1002/sam.11556
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发表时间：
2020-03
期刊：
影响因子：
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通讯作者：
Xiong Lyu;M. Ludkovski
中科院分区：
文献类型：
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作者：
Xiong Lyu;M. Ludkovski
我们为随机实验的高斯过程元模型开发了自适应复制设计。自适应优化是顺序设计优化的自然扩展，随着响应特性的学习、输入的集中和元建模开销的增加，复制的好处也会增加。受学习平均模拟器响应的水平集问题的启发，我们开发了五种新方案：多级分批（MLB），棘轮分批（RB），自适应分批逐步不确定性降低（ABSUR），自适应设计与逐步分配（ADSA）和确定性设计与逐步分配（DDSA）。我们的算法同时（MLB，RB和ABSUR）或顺序（ADSA和DDSA）确定顺序设计输入和相应的重复次数。使用合成示例和定量金融中的应用（通过回归蒙特卡罗的随机期权定价）的说明表明，自适应递归带来了显着的计算速度，建模保真度损失最小。
We develop adaptive replicated designs for Gaussian process metamodels of stochastic experiments. Adaptive batching is a natural extension of sequential design heuristics with the benefit of replication growing as response features are learned, inputs concentrate, and the metamodeling overhead rises. Motivated by the problem of learning the level set of the mean simulator response, we develop five novel schemes: Multi‐Level Batching (MLB), Ratchet Batching (RB), Adaptive Batched Stepwise Uncertainty Reduction (ABSUR), Adaptive Design with Stepwise Allocation (ADSA), and Deterministic Design with Stepwise Allocation (DDSA). Our algorithms simultaneously (MLB, RB, and ABSUR) or sequentially (ADSA and DDSA) determine the sequential design inputs and the respective number of replicates. Illustrations using synthetic examples and an application in quantitative finance (Bermudan option pricing via Regression Monte Carlo) show that adaptive batching brings significant computational speed‐ups with minimal loss of modeling fidelity.