Efficient batch-sequential Bayesian optimization with moments of truncated Gaussian vectors

Understand

We deal with the efficient parallelization of Bayesian global optimization algorithms, and more specifically of those based on the expected improvement criterion and its variants.

• A closed form formula relying on multivariate Gaussian cumulative distribution functions is established for a generalized version of the multipoint expected improvement criterion.
• In turn, the latter relies on intermediate results that could be of independent interest concerning moments of truncated Gaussian vectors.
• The obtained expansion of the criterion enables studying its differentiability with respect to point batches and calculating the corresponding gradient in closed form.