Autoencoder-enhanced joint dimensionality reduction for constrained Bayesian optimisation

Abstract Bayesian Optimisation (BO) is a sample-efficient method for optimising expensive black-box functions, making it particularly suitable for engineering problems where gradients are unavailable and evaluating the objective or constraints is computationally costly. However, such problems often involve high-dimensional inputs and a large number of constraints, posing significant challenges for standard BO frameworks. While prior research has addressed scalability with respect to high-dimensional inputs in constrained settings, efficiently handling large numbers of constraints, i.e. high-dimensional outputs, remains an open problem. This work introduces A utoencoder- E nhanced Joint Dimensionality R eduction for C o nstrained BO (AERO-BO), a framework that performs dimensionality reduction in both the input (design variable) and output (objective and constraint) spaces via autoencoders. These autoencoders are trained online, requiring no pre-training, and their respective latent representations are connected through Gaussian Processes, which serve as surrogate models during optimisation. By operating in a joint latent space, AERO-BO enables scalable and efficient optimisation in settings with hundreds of design variables and thousands of black-box constraints.