Adaptive Batching for Gaussian Process Surrogates with Application in Noisy Level Set Estimation
This work addresses the computational bottleneck in noisy level set estimation for stochastic simulators, offering incremental improvements to existing sequential design methods.
The authors tackled the problem of efficiently learning level sets in stochastic experiments by developing adaptive batching schemes for Gaussian process surrogates, resulting in significant computational speed-ups with minimal loss of modeling fidelity in synthetic and financial applications.
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 four 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.