  Bayesian Optimization (BO) is a technique for sample-efficient black-box
optimization that employs probabilistic models to identify promising input
locations for evaluation. When dealing with composite-structured functions,
such as f=g o h, evaluating a specific location x yields observations of both
the final outcome f(x) = g(h(x)) as well as the intermediate output(s) h(x).
Previous research has shown that integrating information from these
intermediate outputs can enhance BO performance substantially. However,
existing methods struggle if the outputs h(x) are high-dimensional. Many
relevant problems fall into this setting, including in the context of
generative AI, molecular design, or robotics. To effectively tackle these
challenges, we introduce Joint Composite Latent Space Bayesian Optimization
(JoCo), a novel framework that jointly trains neural network encoders and
probabilistic models to adaptively compress high-dimensional input and output
spaces into manageable latent representations. This enables viable BO on these
compressed representations, allowing JoCo to outperform other state-of-the-art
methods in high-dimensional BO on a wide variety of simulated and real-world
problems.
