Conditional simulation for efficient global optimization

A classic Kriging or Gaussian process (GP) metamodel estimates the variance of its predictor by plugging-in the estimated GP (hyper)parameters; namely, the mean, variance, and covariances. The problem is that this predictor variance is biased. To solve this problem for deterministic simulations, we propose “conditional simulation” (CS), which gives predictions at an old point that in all bootstrap samples equal the observed value. CS accounts for the randomness of the estimated GP parameters. We use the CS predictor variance in the “expected improvement” criterion of “efficient global optimization” (EGO). To quantify the resulting small-sample performance, we experiment with multi-modal test functions. Our main conclusion is that EGO with classic Kriging seems quite robust; EGO with CS only tends to perform better in expensive simulation with small samples.