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Adaptive Batching for Gaussian Process Surrogates with Application in Noisy Level Set Estimation (306685)Mike Ludkovski, University of California, Santa Barbara
*Xiong Lyu, University of California, Santa Barbara
Keywords: Gaussian process surrogates, stochastic simulation, level set estimation, quantitative finance
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, input sites concentrate, and the metamodeling overhead rises. Motivated by the problem of learning the level set of the mean simulator response we develop three novel schemes: Multi-Level Batching, Ratchet Batching, and Adaptive Batched Stepwise Uncertainty Reduction (ABSUR). Our algorithms simultaneously determine the sequential design sites 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.