Adaptive batching for Gaussian process surrogates with application in noisy level set estimation. (16th October 2021)

• Record Type: Journal Article
• Authors: Lyu, Xiong; Ludkovski, Michael
• Is Part Of: Statistical analysis and data mining. Volume 15:Number 2(2022)
• Page Start: 225
• Page End: 246
• Publication Date: 2021-10-16
• Subjects: design of experiments -- GP surrogates -- level set estimation -- stepwise uncertainty reduction -- stochastic simulation; Data mining -- Statistical methods -- Periodicals; 006.312
• DOI: 10.1002/sam.11556
• Languages: English
• ISSNs: 1932-1864

Abstract

Abstract: 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.