Process-constrained batch Bayesian optimisation

Abstract Prevailing batch Bayesian optimisation methods allow all the control variables to be freely altered at each iteration. Real-world experiments, however, have physical limitations making it time-consuming to alter all settings for each recommendation in a batch. This gives rise to a unique problem in BO: in a recommended batch, a set of variables that are expensive to experimentally change need to be constrained and the remaining control variables are varied. We formulate this as process-constrained batch Bayesian optimisation problem. We propose algorithms pc-BO and pc-PEBO and show that the regret of pc-BO is sublinear. We demonstrate the performance of both pc-BO and pc-PEBO by optimising benchmark test functions, tuning hyper-parameters of the SVM classifier, optimising the heat-treatment process for an Al-Sc alloy to achieve target hardness, and optimising the short nano-fiber production process.