A Quadrature Approach for General-Purpose Batch Bayesian Optimization
  via Probabilistic Lifting
Masaki Adachi Satoshi Hayakawa Martin Jørgensen Saad Hamid Harald Oberhauser Michael A. Osborne
Parallelisation in Bayesian optimisation is a common strategy but faces
several challenges: the need for flexibility in acquisition functions and
kernel choices, flexibility dealing with discrete and continuous variables
simultaneously, model misspecification, and lastly fast massive
parallelisation. To address these challenges, we introduce a versatile and
modular framework for batch Bayesian optimisation via probabilistic lifting
with kernel quadrature, called SOBER, which we present as a Python library
based on GPyTorch/BoTorch. Our framework offers the following unique benefits:
(1) Versatility in downstream tasks under a unified approach. (2) A
gradient-free sampler, which does not require the gradient of acquisition
functions, offering domain-agnostic sampling (e.g., discrete and mixed
variables, non-Euclidean space). (3) Flexibility in domain prior distribution.
(4) Adaptive batch size (autonomous determination of the optimal batch size).
(5) Robustness against a misspecified reproducing kernel Hilbert space. (6)
Natural stopping criterion.