Adaptive Batching for Gaussian Process Surrogates with Application in Noisy Level Set Estimation

Metamodels offer a cheap statistical representation of complex and/or expensive stochastic simulators that arise in applications ranging from engineering to environmental science and finance [Santner et al., 2013]. Gaussian process (GP) frameworks have emerged as the leading family of metamodels thanks to their flexibility, analytical tractability and superior empirical performance. However, for GP metamodels to be fast, it is imperative to keep the respective design size A manageable. In particular, unless the simulator is truly expensive or the input domain is vast, the typical recommendation is to restrict to hundreds of inputs, A 10 3 . This creates a major tension as frequently the stochastic simulator has low signal-to-noise ratio or a complex noise structure. A prototypical example is where the simulator Y (x) F (X [0, t]) X0 x involves functionals of a continuous-time Markov chain or stochastic differential equation solution (X t), whereby the stochasticity tends to dominate the trend/drift term for short t, and moreover simulation noise is non-Gaussian and state-dependent (heteroskedastic). Both authors are partially supported by NSF DMS-1521743.