Autoencoder-Enhanced Joint Dimensionality Reduction for Constrained Bayesian Optimisation

Abstract Bayesian Optimisation is a sample-efficient method for optimising black-box functions, making it ideal for engineering problems where gradients are unavailable and evaluating the objective and constraints is computationally expensive. However, these problems often involve high-dimensional inputs and a large number of constraints, posing significant challenges. While prior research has scaled Bayesian Optimisation to high-dimensional inputs in constrained settings, additionally handling numerous constraints (high-dimensional outputs) introduces further difficulties. This work presents Autoencoder-Enhanced Joint Dimensionality Reduction for Constrained Bayesian Optimisation (AERO-BO), a framework that uses autoencoders to reduce dimensionality in both input space (design variables) and output space where the outputs which include the objective and constraint values. The respective latent spaces are connected by Gaussian Processes, which act as the surrogate models during optimisation. By leveraging this approach, AERO-BO offers a scalable and efficient solution for high-dimensional input-output problems, accommodating hundreds of design variables and thousands of constraints to efficiently address complex engineering optimisation challenges.