Replication or Exploration? Sequential Design for Stochastic Simulation Experiments

• Activity Number: 600 - Less Can Be More: Smart Sampling in Data and Engineering Sciences
• Type: Topic Contributed
• Date/Time: Thursday, August 1, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Robert Gramacy* and Mickael Binois and Jiangeng Huang and Mike Ludkovsku
• Companies: Virginia Tech and Argonne National Laboratory and Virginia Tech and UC Santa Barbara
• Keywords: computer experiment; Gaussian process; surrogate model; input-dependent noise; replicated observations; lookahead

Abstract

In this paper we investigate the merits of replication, and provide methods that search for optimal designs (including replicates), in the context of noisy computer simulation experiments. We first show that replication offers the potential to be beneficial from both design and computational perspectives, in the context of Gaussian process surrogate modeling. We then develop a lookahead based sequential design scheme that can determine if a new run should be at an existing input location (i.e., replicate) or at a new one (explore). When paired with a newly developed heteroskedastic Gaussian process model, our dynamic design scheme facilitates learning of signal and noise relationships which can vary throughout the input space. We show that it does so efficiently, on both computational and statistical grounds. In addition to illustrative synthetic examples, we demonstrate performance on two challenging real-data simulation experiments, from inventory management and epidemiology.